TTUi 



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AN C/ 



ELEMENTARY COURSE 



Civil Engineering 



FOR THE USE OF 



CADETS OF THE UNITED STATES MILITARY ACADEMY. 



Prof. J. B. WHEELEE. 






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Kfe^^ 





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AN 



ELEMENTARY COU 




Civil Engineering 



FOR THE USE OP 



CADETS OF THE UNITED STATES MILITARY ACADEMY. 



BY 

J. B. WHEELER, 



Professor of Civil and Military Engineering in the United States Military Academy at 
West .Point, JS r . Y., and Bret: fit- Colon el U. S. Army. 



New York : 
PRINTED FOR THE U. S. MILITARY ACADEMY, 



D. VAN NOSTRAND, 
23 Murray Street and 27 Warren Street. 

1874. 






Transfer 
Engineers School Uby. 
June 29,1931 



^ 



£ 



INTRODUCTORY CHAPTER. 



k 



I. Engineering is the term employed to denote the science and art 
of utilizing the forces and materials of nature. 

It is generally divided into two principal branches, Civil and Military 
Engineering. 

The latter embraces the planning and construction of all defensive 
and offensive works used in military operations. 

The former comprises the designing and building of all works in- 
tended for the comfort of man or to improve the country, either by 
beautifying it or increasing its prosperity. 

In this branch the constructions are divided into two classes, according 
as the parts of which they are made are intended to rest or to move rela- 
tively with respect to each other. In the former case; they are known as 
structures, and in the latter as machines. 

II. It is usual to limit the term civil- engineering to the planning and 
construction of works of the first class, and to use the term mechanical 
or dynamical engineering when machines are the works considered. 

It is also usual to subdivide civil engineering into classes, according to 
the prominence given to some one or more of its parts upon applying them 
in practice, as topographical engineering, hydraulic engineering, railway 
engineering, etc. By these divisions greater progress to perfection is 
assured. Notwithstanding this separation into branches and subdivisions, 
there are certain general principles common to them all. 

III. The object of the following pages is to give in regular order those 
elementary principles common to all branches of engineering which are 
essential for the student to learn, that he may understand the nature of the 
engineer's profession, and know how to apply the principles that he has 
already acquired. 

IV. A structure is a combination of portions of solid materials so 
arranged as to withstand the action of any external forces to which it may 
be exposed, and still preserve its form. These portions are called pieces, 



and the surfaces where they touch and are connected are called joint*. To 
distinguish the term solid here used, from the purely geometrical one, or 
from those that are fluid, the term is applied to a body that offers an appre- 
ciable resistance to the action of the different forces to which it may be 
subjected. 

V. The entire structure rests on a part of the solid material of the earth, 
which is called the foundation or bed of the foundation of the structure. 

VI. The permanence of a structure requires that it should possess 
stability, strength, and stiff a ess. 

It will possess these when the following conditions are fulfilled : 

When all the external forces acting on the whole structure are in 
equilibrium ; 

When those acting on each piece are in equilibrium ; 

When the forces acting on each of the parts into which a piece may be 
conceived to be divided are in equilibrium ; and 

When the alteration in form of any piece caused by the external forces 
does not pass certain prescribed limits. 

A knowledge, therefore, of the forces acting on the structure, and of 
the properties of the materials to be used in its construction, is essential. 

VII. The designing and building of a structure form three distinct 
operations, as follows : 

1. The conception of the project or plan ; 

2. Putting this on paper, so it can be understood ; and 

3. Its execution. 

The first requires a perfect acquaintance with the locality where the 
structure is to be placed, the ends or objects to be attained by it, and the 
kind and quantity of materials that can be supplied at that point for its 
construction. 

The x cond requires thai the projector should know something of draw- 
ing, as it is only by drawings and models, accompanied by descriptive 
memoirs, with estimates of cost, thai the arrangement and disposition of 
the various parts and the expense of a proposed work can be understood 
i»\ others. 

The draw IngS arc respect ively called the plan, elevation, and cross- 

section, according to the parts they represent. A symmetrical structure 
requires but few drawings; one not symmetrical, or having different 

fronts, w ill require a greater number. 

I ||r e, i" be understood, must be accompanied b\ written specifications 



explaining fully all the parts. The estimate of cost is based upon the cost 
of the materials, the price of labor, and the time required to finish the 
work: 

The third may be divided into three parts : 

1. The field-work, or laying out the work ; 

2. The putting together the materials into parts ; and 

3. Combining these parts in the structure. 

These require a knowledge of surveying, levelling, and other operations 
incident to laying out the work ; 

A knowledge of the physical properties of the materials used ; 

The art of forming them into the shapes required, and 

How they should be joined together to best satisfj^ the conditions that 
are to be imposed upon the structure. 

VIII. In planning and building a structure, the engineer should be 
governed by the following conditions : 

That the structure possesses the necessary strength ; that it will last the 
required time; and that its cost wilt be reasonable. In other words, the 
engineer in projecting and executing a work should duly consider the 
elements of strength, durability, and economy. 



ELEMENTARY COURSE 



CIVIL ENGINEERING. 



PART I. 

BUILDING MATERIALS. 

1. The materials in general use for civil constructions may be arranged 
in three classes : 

1st. Those which constitute the more solid components of structures, 
;is Stone, Brick, Wood, and the Metals; 

2d. The cements in general, as Mortar, Mastics, Glue, etc., which are 
used to unite the more solid parts ; and 

3d. The various mixtures and chemical preparations, as solutions of 
Salts, Paints, Bituminous Substances, etc., employed to coat the more 
solid parts and protect them from the action of the weather and other 
causes of destructibility. 

CHAPTER I. 
STONE. 

2. The qualities required in stone for building purposes are so various 
ili.it no very precise directions can be given thai would exactly meei any 
particular case. Whai would be required for a sea-wall would not answer 
for ;• dwelling-house. In most cases the choice is limited by the cost. 
'II: iii"i e Bential properties of stone as a building-material are strength, 
fiardness, durability, ami ease of working. These properties are deter- 
mined by experience or actual experiment. 

;:. The term Stone <>r Bock is applied to any aggregation o\' several 

mineral lib tances, and For the convenience of description may be ar- 

d under three general heads— the 8Uieiou8 t the argillaceous, and the 



I. — SILICIOUS STONES. 

4. Silicious stones are those in which silica is the principal constituent. 
With a few exceptions, their structure is crystalline-granular, the grains in 
them being hard and durable. They emit sparks when struck with a steel , 
and generally do not effervesce with acids. 

5. Some of the principal silicious stones used in building are Syenite, 
Granite, Gneiss, Mica Slate, Hornblende Slate, Steatite, and the Sandstones. 
For their composition, particular description, etc. , see any of the manuals 
of mineralogy. 

G. Syenite, Granite, and Gneiss.— These stones differ but little in the 
essential qualities for a good building material, and from the great resem- 
blance of their external characters and physical properties are generally 
known to builders by the common term granite. 

Granite (Syenite, Granite, and Gneiss).— This stone ranks high as a 
building material, in consequence of its superior strength, hardness, and 
durability, furnishing a material particularly suitable for structures which 
require great strength. It does not resist well very high temperatures, and 
its great hardness requires practised stone-cutters to be employed to work 
it into proper shapes. It is principally used in works of magnitude and 
importance, as light-houses, sea-walls, revetment-walls of fortifications, 
large public buildings, etc. It is only in districts where it abounds that it 
is used for ordinary dwelling-houses. It was much used by the ancients, 
especially by the Egyptians, some of whose structures are still remaining 
in good condition, so far as the stone is concerned, after 3,000 years' 
exposure. Granite occurs in extensive beds, and may be obtained from 
the quarries in blocks of almost any size that may be required. Gneiss, in 
particular, from the mica being more in layers, which gives it a stratified 
appearance, admits of being broken out into thin slabs or blocks. A 
granite selected for building purposes should have a fine grain, even 
texture, and the constituents of which it is composed uniformly disse- 
minated through the mass. It should be free from pyrites or any iron ore, 
which on exposure to the weather will rust and deface, if not destroy, the 
stone. The feldspathic varieties are the best, and the syenitic are the most 
durable. An examination of the rock in and around the quarry may give 
some idea of its durability. 

7. Mica Slate has the same materials in its composition as gneiss, and 
breaks with a glistening or shining surface. The compact varieties are 
much used for flagging, for door and hearth stones, and often for lining 



furnaces, as it can be broken out in thin, even slabs. In districts where it 
abounds it is often used in ordinary masonry work. 

8. Hornblende Shite resembles mica slate, but is tougher, and is an 
excellent material for flagging. 

9. 8U utile or Soapstone is a soft stone, easily cut by a knife, and greasy 
to the touch. From the ease with which it is worked, and its refractory 
nature, it is used for tire-stones in furnaces and stoves, and for jambs in 
fire-places. Being soft, it is not suitable for ordinary building purposes. 

10. Sandstone is a stratified rock consisting of grains of silicious sand 
arising from the disintegration of silicious stones cemented together by 
some material, generally a compound of silica, alumina, and lime. It has 
a harsh feel, and every dull shade of color from white through yellow, 
red, and brown to nearly black. Its strength, hardness, and durability 
vary between very wide limits ; some varieties being little inferior to good 
granite as a building-stone, others being very soft, friable, and disin- 
tegrating rapidly when exposed to the weather. The least durable sand- 
stones are those which contain the most argillaceous matter; those of a 
feldspathic character are also found not to withstand well the action of the 
weather. The best sandstone lies in thick strata, from which it can be cut 
in blocks that show very faint traces of stratification ; that which is easily 
split into thin layers is weaker. It should be firm in texture, not liable to 
peel off on exposure, and be free from pyrites or iron-sand, as these rust 
and disfigure the blocks. It is generally porous and capable of absorbing 
much water, hut it is comparatively little injured by moisture, unless when 
built with iis layers set on edge. In this case the expansion of water in 
fre >zing between the layer-; makes them split or "scale" off. It should be 
built with the strata in a horizontal position, so that any water which may 
penetrate between the layers lias room to expand or escape. It is used 
very extensively as a building-stone, for flagging, for road materials, ami 

s ■ of it- varieties furnish an excellent tire-stone. Most of the varieties 

of sandstone yield readily under the ehisel and saw, and split evenly, and, 
from these properties, have received from workmen the name of 
lr, , slum . 

1 1. other varieties of silicious stones besides those named, as porphyry, 
trap or greenttone, basalt, quartz-rock (cobble-stone), buhr-stone, etc., are 
" ed for building ami engineering purposes, and are eminently tit, either 

Qe or rubble, bo far a- strength and durability are concerned. 



ARGILLACEOUS STONES. 

12. Argillaceous or Clayey Stones are those in which alumina exists in 
sufficient quantity to give the stone its characteristic properties. 

Roofing Slate is the most important variety of building-stone of this 
class. It is a stratified rock of great hardness and density, commonly of a 
dark dull blue or purplish color. To be a good material for roofing it should 
split easily into even slates, and admit of being pierced for nails without 
fracturing. It should be free from everything that can undergo decom- 
position on exposure. The signs of good quality in slate are compactness, 
smoothness, and uniformity of texture, clear dark color, give a ringing 
sound when struck, and absorb but little water. 

Being nearly impervious to water, it is principally used to cover roofs, 
line water-tanks, and for similar purposes. 

CALCAREOUS STONES. 

13. Calcareous Stones are those in which calcium monoxide or lime is 
the principal constituent. It enters as a sulphate or carbonate. 

14. Calcium Sulphate, known as gypsum in its natural state, when 
burnt and ground up forms a white powder known as plaster-of-Paris. 
This powder, being mixed with a little water, becomes, on drying, hard 
and compact. Gypsum is not used as a building-stone, being too soft. 
The plaster, owing to its snowy whiteness, translucency, and fine texture, 
is used for taking casts, making models, and for giving a hard finish to 
walls. Care must be taken to use it only in dry and protected situations, 
as it absorbs moisture freely, then swells, cracks, and exfoliates rapidly. 

15. Calcium Carbonates, or lime-stones, furnish a large amount of ordi- 
nary building-stone, ornamental stones, and the principal ingredient in the 
cements and mortars. 

They' are distinguished by being easily scratched with a knife, and by 
effervescing with an acid. In texture they are either compact or granu- 
lar ; in the former the fracture is smooth, often conchoidal ; in the latter a 
crystalline-granular surface, the fine varieties resembling loaf-sugar. 

The lime-stones are generally impure carbonates, and we are indebted 
to these impurities for some of the most beautiful as well as the most in. 
valuable materials used for constructions. Those which are colored by 
metallic oxides, or by the presence of other minerals, furnish the large 
number of colored and variegated marbles, while those which contain a 



10 



certain proportion of impurities, as silica, alumina, etc., yield, on calcina- 
tion, those cements which, from their possessing the property of hardening 
under water, have received the names of hydraulic lime, hydraulic 
cement, etc. As a building material, they are classed into two divisions — 
those that receive a polish, and those that do not — which are known as 
marbles and common limestones. 

16. Marbles. — Owing to the cost of preparing them, and the high polish 
of which they are susceptible, the marbles are mostly reserved for orna- 
mental buildings and purposes. 

They present great variety, both in color and appearance, and have 
generally received some appropriate name descriptive of these accidents. 

Statuary Marble is of the purest white, finest grain, and free from all 
foreign minerals. It receives that delicate polish without glare which 
admirably adapts it to the purposes of the sculptor, for whose uses it is 
mostly reserved. 

Conglomerate Marble. — This consists of two varieties ; the one termed 
pudding stone, which is composed of rounded pebbles embedded in com- 
pact lime-stone ; the other termed breccia, consisting of angular fragments 
united in a similar manner. The colors of these marbles are generally 
variegated, forming a very handsome ornamental material. 

Bird's-eye Marble. — The name of this stone is descriptive of its appear- 
ance, which arises from the cross-sections of a peculiar fossil (fucoides 
demissus) contained in the mass, made in sawing or splitting it. 

Lumachtlla Marble. — This is obtained from a lime-stone having shells 
embedded in it, and takes its name from this circumstance. 

Verd Anil [tie. — This is a rare and costly variety, of a beautiful green 
color, caused by veins and blotches of serpentine diffused through the 
lime-stone. 

There are many other varieties that receive their name either from their 
appearance or the localities from which they are obtained. 

Many of these are imitated by dealers, who Btain the common marbles, 
by processes known to themselves, so successfully as to require a close 
examination t<> distinguish them from the real. 

i; Common Linn Stones. — These furnish a great variety of building- 

which present -rem diversityin their physical properties. Some 

(•f them s.cm us durable as the best silicious stones, and are but little 

Inferior to them in strength and hardness; others decompose rapidly on 

exposure I" the Weather; and some kinds are so soft that, when firs! 



V 



11 



quarried, they can be scratched with the nail and broken between the 
fingers. Their durability is materially affected by the foreign minerals 
they may contain ; the presence of clay injures the stone, particularly 
when, as sometimes happens, it runs through the bed in very minute veins ; 
blocks of stone having this imperfection soon separate along these veins 
on exposure to moisture. Ferrous oxide, sulphate, and carbonate of iron, 
when present, are also very destructive in their effects, frequently causing 
by their chemical changes rapid disintegration. 

Among the varieties of impure carbonates of lime are the magnesia n 
lime-stones, called dolomites. They are regarded in Europe as a superior 
building material ; those being considered the best which are most crys- 
talline, and are composed of nearly equal proportions of the carbonates of 
lime and magnesia. Some of the quarries of this stone which have been 
opened in New York and Massachusetts have given a different result ; the 
stone obtained from them being, in some cases, extremely friable. 

ARTIFICIAL STONES. 

18. The term Artificial Stone is applied to any composition to which, 
by an artificial process, the general properties of natural stone are imparted. 
Yarious attempts from time to time have been made to make an imitation 
which, possessing all the merits, and being free from the defects, of the 
most useful building-stones, would supplement, if not supersede, them. 

For a brief description of some of them and their mode of manufacture 
see paragraphs 116 to 120. 

GENERAL OBSERVATIONS ON THE PROPERTIES OF STONE AS A BUILDING 

r 

MATERIAL. 

19. Strength, hardness, durability, and ease of working have already 
been mentioned as essential properties to be considered in stone to be 
selected for building purposes. 

It is not easy to judge of the qualities from external appearances. In 
most cases stone which has one of the three properties first named will 
have also the other two. In general, when the texture is uniform and com- 
pact, the grain fine, the color dark, and the specific gravity great, the stone 
is of good quality. If there are cracks, cavities, presence of iron, etc.. 
even though it belong to a good class of stone, it will be deficient in some 
of these essential qualities, and should be rejected. A coarse stone is ordi- 



12 



narily brittle, and is difficult to work ; it is also more liable to disintegrate 
than those of a finer grain. 

20. Strength. — Among stones of the same kind, that which has the 
greatesl heat iness is almost always the strongest. 

As stone is ordinarily to be subjected only to a crushing force, it will 
only be in particular cases that the resistance to this force need be consid- 
ered, as the strength of stone in this respect is ordinarily greater than is 
generally required of it. If its durability is satisfactorily proved, as a rule, 
its strength may be assumed as sufficient. 

21. Hardness. — This property is easily ascertained by actual experi- 
ment and a comparison made with other stones wliose qualities have been 
tested. It is an essential quality in stone exposed to wear from attrition. 
Stones selected for paving, flagging, and steps for stairs should be hard 
and of a grain sufficiently coarse not to admit of becoming very smooth 
under the action to which they are submitted. 

By the absorption of water stones become softer and more friable. 
The materials for road coverings should be % selected from those stones 
which absorb least water, and are also hard and not brittle. Granite and 
varieties, lime-stone, and common sand-stone do not make the best 
materials for roads of broken stone. All the hornblende rocks, porphyry, 
compact feldspar, and the quartzose rock associated with graywacke, fur- 
nish good, durable road coverings. The fine-grained granites which contain 
hut a small proportion of mica, and the fine-grained silicious sand-stones 
which arc free from clay, form a durable material when used in blocks for 
paving. Mica slate, talcose slate, hornblende slate, some varieties of gneiss, 
some varieties <>r sand-stone of a slaty structure, and graywacke slate, 
yield excellent materials for flag-stone. 

22. Durability. — By this term is meant the power to resist the wear and 
Prom atmospheric causes when exposed to their influence, the capa- 
city to sustain high temperature, and the resistance to the destructive 
action of fresh and salt water. 

The appearances which indicate probable durability are often decep- 
tive. 

genera] rule, those stones of the same Hnd which are fine- 
ted, absorb least water, and are of greatest specific gravity, an 

| durable under ordinary exposures. The weight of a stone, how. 

may arise from a large proportion of metallic oxide - a circumstai 

linfai oiaUe In il durahilil v. 



18 



The various chemical combinations of iron, potash, and clay, when 
found in considerable quantities, both in the primary and sedimentary 
silicious rocks, greatly affect their durability. The potash contained in 
feldspar dissolves, and, carrying off a considerable proportion of the 
silica, leaves nothing but aluminous matter behind. The clay, on the 
other hand, absorbs water, becomes soft, and causes the stone to crumble 
to pieces. 

24. Frost, or rather the alternate actions of freezing and thawing, is the 
most destructive agent of nature with which the engineer has to contend. 
Its effects vary with the texture of stones ; those of a fissile nature usually 
splitting, while the more porous kinds disintegrate, or exfoliate at the 
surface. When stone from a new quarry is to be tried, the best indication 
of its resistance to frost may be obtained from an examination of any 
rocks of the same kind, within its vicinity, which are known to have been 
exposed for a long period. Submitting the stone fresh from the quarry to 
the direct action of freezing would seem to be the best test, if it were not 
that some stones, which are much affected by frost when first quarried, 
splitting under its action, become impervious to it aftei fchey have lost the 
moisture of the quarry, as they do not reabsorb near so large an amount 
as they bring from the quarry. 

25. A test for ascertaining the probable effects of frost on stone was in- 
vented by M. Brard, a French chemist, which can be used for determining 
the probable comparative durabilities of specimens. It is to imitate the dis- 
integrating action of frost by means of crystallization of sodium sulphate. 
The process may be stated briefly as follows : Let a cubical block, about 
two inches on the edge, be carefully sawed from the stone to be tested. 
A cold saturated solution of the sodium sulphate is prepared, placed over 
a fire, and brought to the boiling-point. The stone, having been weighed, 
is suspended from a string, and immersed in the boiling liquid for thirty 
minutes. It is then carefully withdrawn, the liquid is decanted free from 
sediment into a flat vessel, and the stone is suspended over it in a cool 
cellar. An efflorescence of the salt soon makes its appearance on the 
stone, when it must be again dipped in the liquid. This should be done 
once or more frequently during the day, and the process be continued in 
this way for about a week. The earthy sediment found at the end of this 
period in the vessel is carefully weighed, and' its quantity will give an 
indication of the like effect of frost. This process is given in detail in 
Vol. XXXVIII. Annates cle Chemie et de Physique. 



14 



This test, having corresponded closely with their experience, has re- 
ceived the approval of man}' French architects and engineers. Experi- 
ment, however, made on some of the more porous stones, by exposing 
them to the alternate action of freezing and thawing, gave results very 
different from those obtained by Brard's method., 

26. The wear of stone from ordinary exposure is very variable, depend- 
ing not only upon the t3xture and constituent elements of the stone, but 
also upon the locality and the position it may occupy in a structure with 
respect to the prevailing driving rains. This influence of locality on the 
durability of stone is very marked. Stone is observed to wear more 
rapidly in cities than in the country, and the stone in those parts of edi- 
fices exposed to the prevailing rains and winds soonest exhibits signs of 
decay. The disintegration of the stratified stones placed in a wall is 
mainly affected by the position which the strata or laniinoe receive with 
respect to the exposed surface ; proceeding faster when the faces of the 
strata are exposed, which is the case when the error is committed of not 
1 mill ling in the stones with their laminae lying horizontally. 

27. The only sure test, however, of the durability of any kind of stone, 
is experience. 

28. Stones are often exposed to the action of high temperatures, as in 
the case of great conflagrations. This quality should be looked for in 
using stone for building purposes under such circumstances. They are also 
used to protect portions of a building from great heat, and sometimes to 
line furnaces. Those that resist a high degree of heat are termed. ///v- 
Btoiws. A good (ire-stone should not only be infusible, but also not liable 
to crack or exfoliate from heat. Stones that contain lime or magnesia, 
excepl in the form of silicates, are usually unsuitable. There are several 
varieties of sandstone which, from their being free from feldspar, uncrys- 
tallized, BOmewhal porous, hard, and gritty, are suitable. Talcose slate 
i- often a good fire-stone. 

29. Expansion of Stone f nun fftat. — Experiments have been made in 
this country and Great Britain to ascertain the expansion for even degree 
"i Fahrenheit, and tabulated. Within the ordinary ranges of temperature 
the -tone is loo slightly affected by expansion or contraction to cause am 
perceptible change. Professor Bartlett's experiments, however, showed 
that in a long line of coping it was sufficiently great to crush mortar 
between the blocks. 

80 I'r Mention of Stone.— To add to their durability, especially those 



15 



naturally perishable or„ showing signs of decay, various processes have 
been tried or proposed. All have the same end in view, which is to fill the 
pores of the stone when exposed with some substance which shall exclude 
the air and moisture. Paints and oils have been used. Great hopes have 
been expected from the use of soluble glass (silicate of potash), and also of 
silicate of lime. The former, being applied in a state of solution in water, 
gradually hardens, partly through the evaporation of its water, and partly 
through the removal of the potash by the carbonic acid in the air. The 
latter is used by filling the pores with a solution of silicate of potash, and 
then introducing a solution of calcium chloride or lime nitrate. The 
chemical action produces silicate of lime, filling the pores of the natural 
stone. Time and experience will show if the hopes expected from their 
use will be realized. 

31. Ease of Working the Stone. — This property is to a certain extent the 
inverse of the others. The ease with which stone can be cut or hammered 
into shape implies either softness or a Jow degree of cohesiveness between 
its particles. Independent of the cost, which is largely affected by this 
property, it often happens that the qualities in a stone in every other way 
suitable prevent it from being wrought to a true surface and receiving a 
smooth edge at the angles. 

It requires experience and good judgment to strike a medium between 
these conflicting qualities. 

32. Quarrying. — If the engineer should be obliged to get out his own 
stone and open a new quarry, he should pay particular attention to the 
best and cheapest method of getting it out and hauling it to the point 
where it is to be used. In all cases he will, if possible, open the quarry 
on the side of a hill, and arrange the roads leading to and in it with gentle 
slopes to assist the draught of the animals employed. The stone near the 
surface, not being so good as that beneath, is generally discarded. The 
mass or bed of stone being exposed, a close inspection will discover the 
natural joints or fissures along which the blocks will easily part from each 
other. When natural fissures do not exist, or smaller blocks are required 
than those indicated by them, a line of holes is drilled at regular short 
intervals, or grooves are cut in the upper surface of a bed. Then blunt 
steel wedges or pins, slightly larger than the holes, are inserted, which are 
struck sharply and simultaneously with hammers until the block splits off 
from the layer. 

If large masses of stone be required, resort is made to blasting. This 



16 



operation consists in boring the requisite number of holes, loading them 
with an explosive compound, and firing them. The success of blasting 
will depend upon a judicious selection of the position and depth of the 
holes and the proper charges used. It is well to ascertain, by actual ex- 
periments on the particular rock to be quarried, the effect of the charges, 
so as to determine the amount required to produce a good effect, instead 
of trusting, as too often is the case, to an empirical rule or no rule at all. 



CHAPTER II. 
LIMES AND CEMENTS. 



LIMES. 

33. If a lime-stone be calcined, the carbonic acid will be driven off in 
the process, and the substance obtained is generally known as lime. 

This product will vary in its qualities, depending on the degree of purity 
and impurity of the lime-stone. As a building material, the products are 
divided into three principal classes : 

1. Common or fat lime. 

2. Hydraulic i:me. 

3. Hydraulic cement. 

Common lime is sometimes called air-lime, because a paste with water 
or mortar made from it will harden only in the air. 

Hydraulic lime and cement are also called water-limes and cement*, 
because a paste made from them has the valuable property of hardening 
under water. 

( OMMON LIME. 

84. Lime, common lime, air-lime, quick-lime, and caustic lime (synony 
mous terms) is a calcium monoxide, produced whenever any variety 
of pure <>r nearly pure lime-stone is calcined with a heat of sufficient 

Intensity and duration to expel the carbon dioxide or carbonic acid. It i- 

amorphous, Infusible, somewhat spongy, highly caustic, a specific gravity 

'-••■'iid po real avidity for water. On being mixed with an 

equlvalenl Of water, the water is rapidly absorbed with evolution of great 
heal | Hi-' linn- swells, bursts Into pieces, and finally crumbles into a tin. 



white powder, of which the volume is from two and a half to three and a 
half times that of its original bulk. In this condition the lime is said to be 
sliked and ready for use in making mortar. 

85. White chalk and statuary marble are specimens of pure carbonates 
of lime. Those which furnish the lime of commerce are seldom pure. The 
impurities are silica, alumina, magnesia, oxides of iron, manganese, etc., 
amounting sometimes to nearly ten per cent. The purer the lime-stone, 
the larger is the increase of volume or growth of the lime made from it 
in slaking, and the paste made from this lime is unctuous to the sight and 
touch. For which reason they are often called/«£ or rich limes, as distin- 
guished from others not having these qualities, known as poor or meagre 
limes. 

The latter are seldom reduced to an impalpable, homogeneous powder 
by slaking, and are characterized by less growth. They yield a thin 
paste, and are principally used as fertilizers. If it be necessary to use 
them for building purposes, they should be reduced to a fine powder by 
grinding, although they should never be used if it be possible to avoid it. 

HYDRAULIC LIMES. 

36. These occupy an intermediate place between the common limes 
and the hydraulic cements. They are obtained by calcining lime-stones 
in which the impurities, silica, alumina, magnesia, etc. , range from ten to 
twenty per cent. When they contain from ten to twenty per cent, of 
clay homogeneously mixed with carbonate of lime, they are known as 
argillaceous hydraulic lime-stones ; and when this proportion (nearly) is of 
silica, they are called silicious hydraulic lime-stones. 

37. Hydraulic lime sfekes upon being mixed with water more slowly 
than the meagre limes, with slight elevation of temperature, accompanied 
by little or no vapor, and with an increase of volume rarely exceeding one- 
third of its original bulk. This lime after slaking, being mixed into a stiff 
paste, hardens under water. 

38. It is not manufactured in the United States, nor is it known if there 
be any deposits of the argillaceous hydraulic lime-stones in the United 
States capable of furnishing good hydraulic lime. 

39. That made from the argillaceous lime-stone is manufactured in 
several localities in France, notably at Seilley, about seventy miles from 
Paris. The best type of hydraulic lime from the silicious lime-stone is 



18 

thai known as the hydraulic lime of Teil, from the quarries at Teil on the 
Rhone, Department of Ardeche, France. 

HYDRAULIC CEMENT. 

40. If the lime-stone contain more than 20 per cent, and less than 60 
of the impurities before named, the product obtained by calcination is an 
hydraulic cement. 

It will not slake, and when made into a paste will harden or set under 
water. The rapidity of setting and the degree of hardness will vary with 
the homogeneous character of the stone, the proportions into w r hich the 
clay and lime enter, and the intensity and duration of the burning. 

41. There are two general classes, the slow and the quick setting. 

1 1 t he stone contain at least 20, and not more than 22, per cent, of clay, 
and burned at high heat, the product is a heavy, slow T -setting cement. The 
natural Portland cement is an example. 

If there be from 27 to 30 per cent, of clay, and even as high as 35 in 
aome cases, and a moderate burning, the result is a light, quick-setting 
cement. 

The stone that might, with proper burning, have yielded a slow-setting 
cement, burned at a moderate heat, will produce a light, quick-setting 
cement. The Roman cement, that of Vassy, and the hydraulic cements 
ordinarily made in the United States, are examples of the quick-setting 
class. 

42. The proportion existing between the clay and the lime exercises a 
controlling influence on the properties of the hydraulic cements, and, when 
lie proportion of lime is less than 40 per cent., the stone will, upon calci- 
nation, produce neither lime, hydraulic lime, nor hydraulic cement. If 
clay he present in excess, the product is known as calcareous pozzuolana : 
and when tlcre is 10 per cent, of lime or less, simply pozzuolana. 

POZZUOLANAS. 

i:;. Pozzuolana, which gives the name to this class, is a volcanic mate- 
rial, :i bind of tufa, containing about i) percent, of lime, 16 of silica, L5 of 
alumina, and the real other impurities, and is found near Home, Itah. 

li was originally discovered at the fool of Mount Vesuvius, near the 
\ Ulage "i Pozzuoll, w hence Its name. 

li .me nun i exists in a coherent form, hut more frequently in powder 



19 



or coarse, sharp, and angular grains, generally brown in color, running to 
reddish. If lime be added to supply the deficiency, hydraulic properties 
can be imparted. This has been known for centuries, and Vitruvius and 
Pliny both speak of its high qualities and its use by the Romans in the 
marine constructions of their time. 



TRASS OK TERRAS. 

44. This substance resembles pozzuolana, is used in the same manner, 
and possesses the same properties. It is used in Holland, being princi- 
pally obtained from Bonn and Andernach, on the Rhine below Coblentz. 
If any of these exist in the United States, they are not known. 

45. Artificial Pozzvolanas. — They may be prepared by grinding bricks 
that were well burnt to a powder, or by burning brick-clay and grind- 
ing it. 

46. Remits. — From what has been said we may tabulate the products 
obtained by calcining a pure or argillaceous lime-stone as follows : 



Proportions of 








Resulting Products. 


Distinctive Characters of the Pro- 






ducts. 


Lime. 


Clay. 






100 to 90 


to 10 


Common Lime. 


Slakes rapidly, with great heat, 
vapor, and increase of volume. 
Paste made from it will not 
harden under water or in damp 
places excluded from free cir- 
culation of air. 


90 to 80 


10 to 20 


Hydraulic Lime. 


Slakes slowly, with slight in- 
crease of temperature and vol- 
ume, and little or no vapor. 
Paste of it hardens under 
water. 


80 to 40 


20 to 60 


Hydraulic Cement. 


Does not slake. Powdered, can 
be made into a paste without 
sensible increase of volume, 
with little or no heat, and 
hardens under water without 
shrinking. 


40 to 10 


60 to 90 


Calcareous Pozzu- 


Does not slake or harden under 






olana. 


water. 


10 to 


90 to 100 


Pozzuolana. 


Same as preceding. 



The natural hydraulic cements are ordinarily obtained from argillaceous 
lime-stones, and the table just given considers that class of stones in par- 
ticular. 



20 



47. The dolomites, or magnesian lime-stones, when burned at a low 
heat and reduced to a powder, will give a mortar with hydraulic proper- 
ties ; and in general any magnesian lime-stone containing as high as 60 per 
cent, of carbonate of magnesia, if properly burned, will yield an hy- 
draulic cement, whether clay be present or not. 

48. Physical Characters and Tests of Hydraulic Lime- Stones. — The 
simple external characters of a lime-stone, as color, texture, fracture, and 
taste, are insufficient to enable a person to decide whether it belongs to the 
hydraulic class. 

They are generally some shade of drab or of gray, or of a dark 
grayish blue ; have a compact texture ; even or conchoidal fracture ; with 
a clayey or earthy smell and taste. Although the hydraulic lime-stones 
are usually colored, still it may happen that the stone may be white, 
arising from the combination of lime with a pure clay. 

The difficulty of pronouncing upon the class to which a lime-stone 
belongs from its physical properties alone, renders it necessary to resort to 
chemical analysis and experiment to decide the question. 

In making a complete chemical analysis of a lime-stone more skill in 
chemical manipulations is requisite than engineers usually possess ; but a 
person who has the ordinary elementary knowledge of chemistry can 
ascertain the quantity of clay or of magnesia contained in a lime-stone, 
and (knowing this) can pronounce, with tolerable certainty, as to the 
probabilities of its possessing hydraulic properties after calcination. 

Saving ascertained from the proportions that the stone will probably 
furnish a linn; with hydraulic properties, a sample of it should be sub- 
mitted !<> experiment. The only apparatus required for this purpose is a 
crucible thai will hold about a pint, and a mortar and pestle. The bottom 
as well as I he top or cover of I he crucible should be perforated to give an 
ipward current of air and allow the carbonic acid to escape. The stone to 
be tried i- broken into pieces as nearly the same size as possible, not 
exceeding three-fourths of aD inch cube, and placed in the crucible. When 
more than one Bpecimen is to be tried, and a comparison between them 
made, there should be several crucibles. Access being had to an anthra- 
cite coal Are in .in open grate, or other steady tire, the crucibles are em- 
bedded in the lire nnd covered wiili coals, SO that the top and bottom 
portions of their contents will attain simultaneously a bright-red heat, each 

crucible containing the same quantity of stone as nearly as possible. 

Port) li\-- mlnutOfl after the stone has readied a red heat, if there be only 



21 



one crucible, two or three of the fragments are removed ; in forty-five 
minutes afterwards two or three more are taken out, and this repeated 
for four and a half and perhaps six hours, which will be sufficient to 
expel all the carbonic acid. If there be several crucibles, they may be 
removed in the same order. By this means we will have samples of the 
stone that are burnt too much, not enough, and a class between them. 

The specimen, if a cement, will not slake when sprinkled with water. 
Reducing it to a powder in the mortar, mixing it to a stiff paste with 
water, and immersing it in fresh or salt water, the time of setting and 
degree of hardness it attains being noted, an approximate value of the 
cement may be obtained. 



CALCINATION OF LIME-STONE. 

49. The effect of heat on lime-stones varies with the constituent 
elements of the stone. The pure lime-stones will stand a high degree of 
temperature, losing their carbonic acid and water without fusing, while 
the impure become more or less vitrified when the temperature much 
exceeds a red heat. 



MANUFACTURE OF COMMON LIME. 

50. As the object in making common lime is to drive off the water and 
carbonic acid from the stone, many devices have been used to effect it. A 
pile of logs burning in the open air, on which the lime-stone or oyster- 
shells are thrown, has been frequently used to obtain common lime. It is 
generally manufactured by burning the lime-stone in a kiln suitably con- 
structed for the purpose. 

51. Kilns are divided into two classes : 1st, the intermittent kiln, or 
those in which the fuel is all at the bottom, and the lime-stone built up over 
it ; and, 2d, the perpetual or draw-kiln, in which the fuel and the lime-stone 
are placed in the kiln in alternate layers. The fuel used is either wood or 
coal. In the first class one charge of lime is burned at a time, and, when 
the burning is complete, the kiln is completely cleared out previous to 
burning a second ; while in the latter fresh layers of fuel and lime-stone 
are added at the top as the lime is drawn out at the bottom. 

52. The shapes given to the interiors of kilns are very different. The 
object sought is to obtain the greatest uniform heat possible with the 



22 



smallest expenditure of fuel, and for this purpose thick walls are necessary 
to prevent loss of heal by radiation. 

53. The simplest form of kiln is that represented in Fig. 1, in which 
wood is used for fuel. It has a circular horizontal cross-section, and is 
made <>f hammered lime-stone without mortar. 

Fiff. 1. 






mw////A 

WMWA 

mm*. W////M 




ts a vertical section through the axis and arched entrance 
communicating with the interior of a kiln for burning lime with wood; 
'•. <\ '•. 1 ii''-' • pieces of lime-stone forming the arch upon which the mass of 
lime ton< rests; A., arched entrance communicating with the interior. 

Ii i usually placed on the side of a hill, so that the top may be accessi- 
ble for charging the kiln. 

The largesl pieces Of the limestone to be burned are formed into an 
arch, •■. '•• -\ and above this the kiln is filled by throwing the stone in loo < 
] > from the top, the largest first and smaller ones afterwards, and heaping 
1111 '" "i 1 :i hown in the figure. The fuel Issupplied through the arched 
\ 



23 



BURNING. 

54. The management of .the fire is a matter of experiment. For the 
first eight or ten hours it should be carefully regulated, in order to bring 
the stone gradually to a red heat. By applying a high heat at first, or by 
any sudden increase of it until the mass has reached a nearly uniform tem- 
perature, the stone is apt to shiver, and choke the kiln by stopping the 
voids between the courses of stone which form the dome. After the stone 
is brought to a red heat, the supply of fuel should be uniform until the end 
of the calcination. The indications of complete calcination are generally 
manifested by the diminution which gradually takes place in the mass, and 
which, at this stage, is about one-sixth of the primitive volume ; by the 
broken appearance of the stone which forms the dome, the interstices 
between which being also choked up by fragments of the burnt stone ; and 
by the ease with which an iron bar may be forced down through the burnt 
stone in the kiln. When these indications of complete calcination are 
observed, the kiln should be closed for ten or twelve hours to confine the 
heat and finish the burning of the upper strata. 

HORIZONTAL CROSS-SECTION. 

55. The circular seems the most suitable form for the horizontal sections 
of a kiln, both for strength and for economizing the heat. Were the section 
the same throughout, or the form of the interior of the kiln cylindrical, 
the strata of stone, above a certain point, would be very imperfectly 
burned when the lower were enough so, owing to the rapidity with which 
the inflamed gases arising from the combustion are cooled by coming into 
contact with the stone. To procure, therefore, a temperature throughout 
the heated mass which shall be nearly uniform, the horizontal sections of 
the kiln should gradually decrease from the point where the flame rises, 
which is near the top of the dome of broken stone, to the top of the kiln. 
This contraction of the horizontal section from the bottom upward should 
not be made too rapidly, as the draught would be injured and the capacity 
of the kiln too much diminished ; and in no case should the area of the 
top opening be less than about one-fourth the area of the section taken 
near the top of the dome. The proportions between the height and mean 
horizontal section will depend on the texture of the stone, the size of the 
fragments into which it is broken for burning, and the greater Or less ease 
with which it vitrifies. 



24 



REMARKS. 

56. By giving an ovoidal shape to the interior, lining it with fire-brick, 
substituting for the arch of lime-stones a brick one with openings to admit 
a free circulation of air to secure the necessary draught, and arranging it 
with a fire-grate, will give a bettei* kiln than the one shown in Fig. 1. The 
defects of the intermittent kilns are that the stone nearest the fire is liable 
to be injured by over-burning before the top portions are burnt enough, 
and the great waste of fuel. 

57. Perpetual kilns are intended to remedy these defects, especially the 
waste of heat. A simple form of this kiln is shown in Figs. 2 and 3. The 
interior is an inverted frustum of a cone from five to five and a half feet in 

diameter at bottom to nine or ten 
at top, and thirteen or fourteen 
high. It is arranged with three 
entrances for drawing the lime, 
and they are arranged with doors 
to regulate the draught. 

Fig. 2 represents a horizontal 
section made near the base of a 
perpetual lime-kiln for coal. 
a, a, a, arched entrances. 
Fig. 3, vertical section on A 
B through the axis of the kiln. 
58. In these kilns the burning 
is started by first placing a layer of light wood at the bottom, then a layer 
of coal, and then a layer of lime-stone. Layers of coal and lime-stone fol- 
low alternately until the kiln is 
tilled. The lower layer is ig- 
nited, and as the burnt mass 
settles down, and the lime near 

the bottom is sufficiently burnt, 
the drawing commences. 

59. Wood is not so convenient 
a fuel ;i^ coal for this kiln, the 

difficult) <>f distributing it uni- 
formlj and of the same size, and 

quantity ol ash ii forms, being the principal objections. 





25 



60. The perpetual kiln is more economical than the intermittent in the 
use of fuel, but requires more skill and caution in its management. 

The perpetual kiln, invented by Mr. C. D. Page, of Rochester, K Y., 
is used extensively in the western part of New York State and in Maine. 
It is known as a perpetual flame or furnace kiln, arranged for either wood 
or coal, anthracite or bituminous, and avoids the defects arising from 
mixing the fuel and stone together. 

61. Thus far the calcination of those stones producing common lime 
has only been considered. The process of burning lime-stones to produce 
the cements is essentially the same, the intermittent, the perpetual, and 
the furnace kilns being used for the purpose. 

Fig. 4. 





Figs. 4 and 5 represent vertical sections through the axis of the kiln 
and draw-pit of the ordinary perpetual kilns used in the United States for 
burning lime-stone for cement. 

62. The great object of a kiln is to give a cement of good and homoge- 
neous quality with economy of fuel. This uniformity of product is not 
obtained from either the intermittent or perpetual kilns ordinarily used ; 



26 



some of the stone being over-burnt, while other portions, usually the lar- 
gest fragments, arc under-burnt, in some cases partly raw inside. Both of 
these are difficult to reduce to powder, and materially affect the quality of 
the cement. It is very evident that dissimilar stones should not be burned 
together in the same kiln. 

Various kilns have been devised to remedy these defects, and still be 
economical of fuel. The perpetual flame or furnace kiln of Page, before 
named, and the annular or ring kiln, of which the Hoffman is a type, are 
noted examples. 

MANUFACTURE OF THE PRINCIPAL CEMENTS. 

68. The hydraulic cements produced at a low heat are light in weight 
and quick-setting, and never attain, when made into mortar or concrete, 
the strength and hardness of the heavy and slow-setting cements produced 
by burning with heat of great intensity and duration. 

The best example of the latter class is the Portland cement, which is 
made from argillaceous lime-stones containing from 20 to 22 per cent. 
of clay, or from an artificial mixture of carbonate of lime and clay in simi- 
lar proportions. Nineteen-twentieths of all the Portland cement of the 
present day is artificial. It is manufactured extensively throughout 
Europe, either by the wet yrocens, as in England, or the dry £)?yw<?s\<*, as in 
( l-ermany. 

THE WET PROCESS. 

(54. To explain it, the process followed by the works near London is 
taken. The carbonate of lime is furnished by the chalks which are nearly 
pure, and the clay is from the shores of the Medway and Thames, and 
adjoining marshes, being a silicate of alumina containing two parts of 
Bilica to one of all the others, comprising alumina, oxides of iron, etc". 

First The clay and chalk are mixed together in the proper proportions, 
about one to three by weight, in a circular wash-mill, so arranged as to 
thoroughly pulverize the chalk and mix the whole in a semi-fluid, impal- 
pable pa tte 

Second. When the thorough mixture is effected, the liquid, resembling 

whitewash in appearance, is drawn oil' into reservoirs, where it is left to 

-til' The heavier material, or rau cement, settles to the bottom, and 

then the surplus water which is clear is removed. Samples are taken 
from line' I., lime In, in the reservoirs and tested. II' any error he dis- 

1 "\ 1 red in ill'' proportions, ii La corrected. 



27 



Third. When by evaporation the mixture has attained the consistency 
of hard butter or stiff clay, it is removed from the reservoirs to rooms arti- 
ficially heated, and spread out for further drying. 

Fourth. After it has dried sufficiently, it is burned in suitable kilns 
with a white heat, just below the point of vitrification. 

Fifth. The product is then ground between ordinary mill-stones to a 
powder of the necessary fineness. It is then ready for use. 

THE DRY PROCESS. 

65. The carbonate of lime and clay are first kiln-dried at the temper- 
ature of 212° Fahr. , then mixed together in the proper proportions, be- 
tween 20 and 23 per cent, of clay to 80 to 77 per cent, of the carbonate 
of lime, and reduced to a fine powder. This powder is then made into a 
stiff paste, and then into blocks about the size of bricks for burning. The 
bricks are dried and then burnt at a high heat in a kiln and ground to 
powder, as in the preceding case. s 

REMARKS. 

66. It is an easy matter to pulverize the materials, either wet or dry, 
mix them, and then to grind the burnt stone to a powder. 

The difficult part is the proper application and management of the 
heat in burning. The mysterious conversion which takes place in the 
kiln under a heat of sufficient intensity to make glass, is, to some extent 
beyond our control, and to a great extent beyond our knowledge. 

In whatever manner apparently homogeneous lime-stones may be ex- 
posed to burning at a high temperature, it is impossible to avoid the vitri- 
fication of some layers containing too much clay, while others not having 
enough produce cements having lime in excess. For this reason an arti- 
ficial mixture of clay and carbonate of lime is generally relied upon for 
Portland cement. 

67. The superior quality of Portland cement appears to depend greatly 
upon the presence of the double silicate of lime and alumina, which is 
formed only at a high heat. 

LIGHT, QUICK-SETTING CEMENTS. 

• 68. If the lime-stone contain more than 23 per cent, of clay homogene- 
ously distributed through the mass, and is burnt with the same intensity of 
heat and length of time, it generally fuses into a species of slag or glass, 
and is worthless as a cement. 



28 



Hut if the calcination be kept below the point of vitrification, alight, 
quick-setting cement maybe expected. The result appears to be silicate 
and aluminate of lime with uncombined clay, but more especially of silica, 
which, being inert, adulterates and injures the cement. 

A cement of this kind sets quickly under water, but is far inferior to 
the Portland cement in hardness and final strength. Those of Vassy, 
Grenoble, etc., in France, and the English and French Roman cements 
made from nodules of septaria, belong to this class. 

This kind of cement may be made artificially, and was quite extensively 
made before the superior qualities of the Portland cement were known. 

ARGILLO-MAGNESIAN CEMENTS. 

G9. The natural hydraulic cements of the United States are made from 
the lime-stones whose • principal ingredients are carbonate of lime, car- 
bonate of magnesia, and clay. The usual process of manufacture is to 
break the stone into pieces not exceeding twelve or fifteen pounds in 
weight, and burn them in an ordinary kiln, either intermittent or per- 
petual, the latter being generally used when coal is the fuel. After being 
burnt, the fragments are crushed by suitable machinery, and then reduced 
to a powder by grinding. The powder is then packed in barrels and sent 
to market. 

70. These lime-stones cannot be burned with the same intensity and 
duration of heat necessary to make Portland cement without fusing into a 
slag destitute of hydraulic properties. Like those argillaceous lime-stones 
just named, they produce a light, quick-setting cement if properly burned, 
giving a silicate and aluminate of lime and magnesia. 

The cements from the valley of Rondout Creek, Ulster County, known 
as Rosendale cement ; from near ghepherdstown, Va. ; Cumberland, Md. ; 
Louisville, Ky. ; Sandusky, Ohio; I'tiea, 111.; and other localities, are 
made from this stone, and belong to this class of cements. 

The Rosendale cement, which is the most valuable of them, will, under 
favorable Circumstances, attain about one-third of the ultimate strength 
and hardness of the Portland cement. 

bcott's cement. 

H I -Mini! invented by Major Scott, of the Royal Engineers, 

British \iin\, ami is referred to, not for any marked advantages it pos- 
. but for the peculiarity in its mode ( >r manufacture. 



59 



The lime-stone is calcined in the usual manner, producing common lime. 
It is then laid in layers of one and a half to two feet thick over the arches 
of a perforated oven, and brought to a dull glow. The fire is then raked out, 
and iron pots containing coarse, unpurified sulphur, about fifteen pounds 
to each cubic yard of lime, are pushed in on the grate-bars, and the sulphur 
ignited. The oven is closed, so as to pi event the escape of the sulphurous 
vapor. After the sulphur has been consumed, the mass is allowed to cool, 
and then ground to a powder like other cements. 

Why lime treated in this manner should acquire hydraulic properties is 
not fully known. 

MAGNESIAN CEMENT. 

72. Pure carbonate of magnesia, known as magnetite, when burned at a 
cherry-red heat, reduced to powder, and made in a paste, possesses hy- 
draulic properties. If the powder be mixed in a paste with magnesium 
chloride — or a very good substitute for it, bittern, the residue of sea-water 
after the salt has been separated by crystallization — a cement is made 
superior to any other known, not excepting even the Portland, in strength 
and hardness. This calcined magnesite has been patented under the name 
of Union cement. 

TESTS FOE, LEVIES AND CEMENTS. 

73. The manufacture of limes and cements having become a special 
branch of industry in the United States and Europe, the engineer can 
easily obtain the kinds required for his purposes, and will rarely, if ever, 
be placed in a position requiring him to make them. He will be more 
particularly concerned in knowing how to test the samples furnished him, 
so as to be able to make a judicious selection. 

TEST FOB, BOSENDALE CEMENT. 

74. This cement should be ground fine enough so that 90 per cent, of 
it can pass a No. 30 wire sieve of thirty-six wires to the lineal inch both 
ways ; should weigh not less than sixty-eight pounds to the struck bushel, 
loosely measured ; and when made into a stiff paste without sand, should 
sustain, without rupture, a tensile strain of sixty pounds to the square inch 
in cross-section when seven days old, the sample having been six days in 
water. 



so 



TEST FOR PORTLAND CEMENT. 

75. Same degree of fineness as just given ; should weigh one hundred 
and six pounds to the struck bushel, loosely measured ; and under the 
same conditions sustain a tensile strain of one hundred and seventy-eight 
pounds to the square inch in cross-section. 

By testing other varieties their relative value with these can he de- 
termined. 

REMARKS. 

76. The wire test was formerly, and is now, partly used to determine the 
hydraulic activity of samples. It is as follows : The paste was made into 
cakes of one and a quarter inches in diameter and five-eighths of an inch 
thick, and immersed in water of an established temperature (65° F.) The 
i i iiics are then noted which they require before they will bear a wire one- 
twelt'th of an inch in diameter loaded to weigh one-quarter of a pound, 
and one one-twenty-fourth of an inch in diameter weighing one pound, 
supported on their points without depression. 

This wire test, when applied to a cement paste without sand, does not 
give a correct indication of the values of their hydraulic properties. 

77. 1 [ydraulic limes and cements deteriorate by exposure to the air. If 
liable to be kept on hand for several months, they should be stored in a 
tighl building tree from draughts of air, and the casks raised several inches 
above the floor, in case it is a stone or earthen one. 

Cements thai have been injured by age or exposure, may have their 
original energy restored by recalculation. Samples have been restored by 
being submitted to a red heat of one hour's duration. 

Common lime, lor the same reasons, should be preserved in tight ves- 
sels. It is usually sent to market in barrels, and is reduced to powder by 
slaking. The fineness of the powder, its growth, the phenomena of 
slaking, and the degree of onctuousness of the paste made with water, are 
i be tests for good lime. 

SLAKING 1,1 MK. 
i The methods used are classed under three heads ■ l. By dro ceiling ; 
'2, imiu, rsii>/i ; and, :{, apuntaneou* or air slaking. 

The flr*t consists In throwing on the lumpa of lime just as they come 

I ' " I •' ■ kiln 3 i I i j i a i •;• l.» pj luC3 Hi mi to paste. The workmen are 

apl to thro* on more water than is required, hence the name. 

The ■"< i is t(» break the lumps of lime Into pieces ool exceeding an inch 

< h. place them in a basket or other contrivance, and immerse them 






31 



iii water for a few seconds, withdrawing them before the commencement 
of ebullition. A modification of this method is to form heaps of the 
proper size of these broken lumps, and sprinkle a certain quantity of water 
upon the lime, the amount of water being from one-fourth to one-third 
the volume of the lime, and applied from the rose of a watering-pot. 

The thinl is to allow the lime to slake spontaneously by absorbing 
moisture from the surrounding atmosphere. 

79. The first method is the one most generally used in the United 
States. 

The lumps of lime are collected together in a layer from six to eight 
inches deep, in a water-tight box or a basin of sand coated over with lime- 
paste to make it hold water, and the requisite amount of water sufficient to 
reduce the lime to a paste is poured over them. This amount of water is 
approximately determined by a trial of a small quantity of lime before- 
hand. It is important that all the water necessary should be added at the 
beginning. After an interval of five or ten minutes, the water becomes 
heated to the boiling-point, and all the phenomena of slaking follow. 

The workmen are apt to use too much water in the beginning, or, not 
using enough, to add more when the slaking is in progress. In the first 
case the resulting paste will be too thin, and, in the latter, checking the 
slaking will make the product lumpy. 

As soon as the water is poured on the lime it is recommended to cover 
the mass with canvas or boards, or a layer of sand of uniform thickness, 
after the slaking is well under way, may be used. Another recommenda- 
tion is, not to stir the lime while slaking. 

80. Writers disagree as to the relative values of the three methods of 
slaking lime. Supposing that in the first process all the water and no more 
than is required to prodvce a, stiff paste is poured on at the beginning, these 
modes may be arranged in their orders of superiority as follows : 

For fat limes : 1, Drowning, or the ordinary method ; 2, spontaneous 
slaking; and, 3, by immersion. For hylraulic limes: 1, Ordinary 
method ; 2, immersion ; and, 3, spontaneous slaking. 

81. In the matter of cost the first mode has a decided advantage over the 
others. The second is not only expensive from the labor required, but 
difficult from the uncertainty of the period of immersion at the hands of 
the workmen. The third involves the expense of storage-rooms or sheds 
and time, a period from twenty days to even a year being necessary to 
complete the slaking. 



32 



PRESERVATION OP THE LIME AFTER BEING SLAKED. 

82. The paste obtained by the first mode may be preserved any length 
of time if kept from contact with the air. It is usual to put it in tight 
casks, or in reservoirs or trenches covered up with sand will be sufficient. 

The powder from the-second and third modes may be preserved for 
some time by placing it in casks or bins with covers, or in heaps in dry 
sheds, covered over with cloth or dry sand. 

83. General Treussart thought that lime should be used immediately 
after it was slaked. In this country this is the ordinary practice. The 
general opinion of engineers is adverse to this practice, and in some parts 
of Europe it is the custom to slake the lime Vie season before it is used. 

84. The principal use of the limes in the engineer's art is as an ingre- 
dient in the mortars and concretes. 



CHAPTER III. 



MORTARS, CONCRETES, ARTIFICIAL STONES, AND MASTICS. 

85. Calcareous Mortar ready for use is a mixture, in a plastic condition, 
Of Lime, sand, and water. It is used to bind together the solid materials in 
masonry constructions, and to form coatings for the exterior surfaces of 
the walls and the interior of buildings. 

SO. It may be divided into two principal classes — common mortar when 
made of common lime, and hydraulic mortar when hydraulic lime or 
cement is used. 

When mortar is thin tempered or in a fluid state, it is known as 
grout. 

87. Mortar when it hardens is simply an artificial stone, and should 
fulfil the essential conditions already given for stone— viz., should possess 
ttrentfth, hardnm, and durability. These qualities are dependent on the 
quality of the lime or cement employed, the kind and quantity of sand, the 
method and degree of manipulation, and the position, with respeet to 
ure or dryness, in which it is subsequently placed. 

Oommon mortar will onlj partially harden in damp places excluded 
from free Circulation Of air, and qoI at all under water. These conditions 

• ;l "' contrary, favorable to the Induration o\' hydraulic mortars. 






33 



88. Sand is the granular product arising from the disintegration of 
rocks. It may therefore, like the rocks from which it is derived, be 
divided into three principal varieties — the silicious, the calcareous, and 
the argillaceous. 

Sand is also named from the locality where it is obtained, as pit-sand, 
which is procured from excavations in alluvial or other deposits of dis- 
integrated rock ; river-sand and sea-sand, which are taken from the shores 
of the sea or rivers. 

Builders again classify sand according to the size of the grain. The 
term coarse sand is applied when the grain varies between £ and ^ of an 
inch in diameter ; the term fine sand, when the grain is between a x 6 and 
2*4 of an inch in diameter ; and the term mixed sand is used for any mix- 
ture of the two preceding kinds. 

The usual mode of determining the size of the sand to be used is to 
screen it by passing it through sieves of various degrees of fineness. The 
sieves are numbered according to the number of openings in a square 
inch of the wire gauze of which they are made. 

89. The silicious sands, arising from the quartzose rocks, are the most 
abundant, and are usually preferred by builders. The calcareous sands, 
from hard calcareous rocks, are more rare, but form a good ingredient for 
mortar. Some of the argillaceous sands are valuable, as they impart 
to common lime when mixed with it hydraulic properties. 

The property which some argillaceous sands possess of forming with 
common or slightly hydraulic lime a compound which will harden under 
water, has long been known in France, where these sands are termed 
arenes. The sands of this nature are usually found in hillocks along river 
valleys. These hillocks sometimes rest on calcareous rocks or argillaceous 
tufas, and are frequently formed of alternate beds of sand and pebbles. 
The sand is of various colors, such as yellow, red, and green, and seems to 
have been formed from the disintegration of clay in a more or less in- 
durated state. They form, with common lime, an excellent mortar for 
masonry exposed either to the open air or to humid localities, as the 
foundations of edifices. 

90. Pit-sand has a rougher and more angular grain than river or sea 
sand, and, on this account, is generally preferred by builders for mortar 
to be used for brick or stone work. 

River and sea sand are by some preferred for plastering, because they 
are whiter and have a finer and more uniform grain than pit-sand. 



84 



91. The sand used in common mortar should be clean, sharp, and 
neither too coarse nor too fine. 

If it be clean, it may be known by not soiling the fingers when rubbed 
between them ; and if ii be sharp, it can be told by filling the hand and 
closing it firmly, listening to the sounds made by the particles rubbing 
against each other. 

Dirty sand, as well as sea sand, should be washed before using to free 
them from their impurities. 

92. Sand enters mortar as a mechanical mixture, and is 'used to save 
expense by lessening the quantity of lime, to increase the resistance of the 
mortal' to crushing, and to lessen the amount of shrinking during the 
drying of the mortar. 

Ii injures the tenacity of mortar, and if too much be used the mortar 
will crumble to powder when it dries. 

93. The quantity or proportion of sand to the lime varies with the 
quality of the lime and the uses of the mortar. 

Vical gives tor common mortar the proportion of 2.4 parts of sand to 
1 of pure slaked lime in paste by measure. 

The practice of the United States Corps of Engineers has been to add 
from 2.5 to 3.5 in bulk of compact sand to 1 of lime and cement, or 
cement alone, in thick paste, in making hydraulic mortars. 



THE METHOD AND DEGREE OF MANIPULATION. 

94. The ingredients of mortar are incorporated either by manual labor 
or by machinery; the latter method gives results superior to the former. 
The machines used tor mixing mortar are the ordinary pug-mill, like those 
(Fig. B) employed by brickmakers for tempering clay, a grinding-mill 
(Fig. ii, or other pattern suitable for the work. The grinding-mill is a 
better machine than the pug-mill, because it not only reduces the lumps 
which are found in tic most carefully -burnt stone after tiie slaking is 
apparent!} complete, but i; brings the lime to the state of a uniform still' 

paste, which it should receive before the sand is incorporated with it. 

8 represents a vertical section through the avis ( ;1 pug-mill for 
mixing "i- tempering mortar. This mill consists of ;i hooped vessel, of 
the form "i .• conical frustum, which receives the ingredients, and a 



35 




vertical shaft, to which arms with teeth resembling an ordinary rake are 

attached for the purpose of mixing the ingredients. 

„. „ A, A, section of sides of the ves- 

Fig. 6. 

sel. 

B, vertical shaft, to which the 

arms C are affixed. 

D, horizontal bar for giving a 
circular motion to the shaft B. 

E, sills of timber supporting the 
mill. 

F, wrought-iron support, through 
which the upper part of the shaft 
passes. 

Fig. 7 represents a part of a mill 
for crushing the lime and tempering 
the mortar. 

A, heavy wheel of timber or cast 
iron. 

B, horizontal bar passing through the wheel, which at one extremity is 
fixed to a vertical shaft, and is arranged at 
the other (C) with the proper gearing for a 
horse. 

D, a circular trough, with a trapezoidal 
cross-section which receives the ingredients to 
be mixed. The trough may be from 20 to 30 
feet in diameter, about 18 inches wide at top, 
and 12 inches deep, and be built of hard 
brick, stone, or timber laid on a firm founda- 
tion. 

A good example of a grinding-mill is given in Lieut, W. H. Wright's 
"Treatise on Mortars," page 98, in describing the mill used at Fort 
Warren, Boston Harbor. 

The steam mortar-mill, in which the wheels or stones revolved on edge, 
used at Fort Taylor, Key West, Florida, and the mortar-mill of Greyvel- 
dinger, used in Paris, in which a revolving screw performs the mixing, are 
both described in Gillmore's "Treatise on Limes, Cements, and Mortars," 
pp. 196, 197, 198, 199, and 200, as also the Fort Warren mortar-mill above 
alluded to. 




86 



95. Process of making Mortar with the Mill. — The lime-paste is first put 
in the circular trough, and to this is added by measurement about one-half 
of (he sand required for the batch. The mill is set in motion, and the 
ingredients thoroughly incorporated. The remainder of the sand is then 
added, and as much water as may be necessary to bring the mass to the 
proper consistency. 

If it be common mortar that we wish to render hydraulic by adding 
hydraulic cement, this should be added to the lime-paste just before the 
mill is set in motion, except in the case of very quick-setting cement, 
which should not be added until the last portions of sand are thrown in. 

96. Process by Hand. — The measure of sand required for the batch is 
placed on the floor and formed into a basin, in which the unslaked lime is 
placed, the lumps being broken to the proper size. The necessary quantity 
of water is poured on by a hose, watering-pots, or ordinary buckets, and 
the lime stirred as long as vapor is evolved. The ingredients are well 
mixed together with the shovel and hoe, a little water being added occa- 
sionally if the mass be too stiff. It is customary then to heap the mortar 
compactly together, and allow it to remain until ready for use. 

97. The rule in mixing mortar, either by machinery or hand, is to see 
that the lime and sand be thoroughly incorporated or mixed throughout 
the mass. 

98. Setting of Mortars. — A mortar has set when it has become so hard 
that its form cannot be altered without causing fracture. The means of 
ascertaining the set is by the wire test. If the mortar supports the point of 
the wire wiihout depression or penetration, it is assumed that the mortar 
has set. 

9<). Hardness, Durability, and Strength. — The same general rules for 
determining these qualities in stone are applicable to mortars, and, as in 
-tone, experience is the best test. 

The principal causes of deterioration and decomposition of mortars are : 

1. Changes of temperature, producing expansions and contractions. 

2. Alternations of freezing and thawing, producing exfoliations and 
disintegrations of the parts exposed to their influence. 

100. Common mortars which have had time to harden resisl the action 
of severe froste verj well, if they are made rather poor, or with an excess 
"i The proportions should be 21 parts of sand or over in bulk to 
one \ olume of t tie lime in p 

Hydraulic mortars Bel equally well in damp situations and in the open 



37 



air ; and those which have hardened in the air will retain their hardness 
when immersed in water. They also resist well the action of frost, if they 
have had time to set before exposure to it ; but, like common mortars, they 
require to be made with an excess of sand to withstand well atmospheric 
changes. 

101. In applying mortars the materials to be joined should be tho- 
roughly moistened — a point too often neglected — and the surfaces made 
clean. Precautions should be taken to prevent too rapid drying, and the 
mortar should be as stiff as it can be used, and still be in a plastic condition. 

102. To ascertain their strength and compare the qualities of different 
mortars, experiments have been made upon the resistance offered by them 
to cross-strains. 

The usual method has been to subject small, rectangular prisms of mor- 
tar, resting on points of support at their extremities, to a cross-strain ap- 
plied at the centre point between the bearings. 

103. Experiments made upon prisms a year old, which had been ex- 
posed to the ordinary changes of weather, gave the following as the ave- 
rage resistances on the square inch offered by mortars to a force of 
traction ; the deductions being drawn from experiments on the resistance 
to a transversal strain : 

Mortars of very strong hydraulic lime 170 pounds. 

ordinary " " 140 " 

" medium " " 100 " 

' ' common lime 40 " 

(bad quality)... ..10 

104. General Totten, late Chief of Engineers U. S. Army, from his 
experiments on mortars deduced the following general results : 

1. That mortar of hydraulic cement and sand is the stronger and 
harder as the quantity of sand is less. 

2. That common mortar is the stronger and harder as the quantity of 
sand is less. 

3. That any addition of common lime to a mortar of hydraulic cement 
and sand weakens the mortar, but that a little lime may be added without 
any considerable diminution of the strength of the mortar, and with a 
saving of expense. 

4. The strength of common mortars is considerably improved by the 






88 



addition of an artificial pozzuolana, but more so by the addition of an hy- 
draulic cement. 

5. Fine sand generally gives a stronger mortar than coarse sand. 

6. Lime slaked by sprinkling gave better results than lime slaked by 
drowning. A Few experiments made on air-slaked lime were unfavorable 
to that mode of slaking. 

7. Both hydraulic and common mortar yielded better results when 
made with a small quantity of water than when made thin. 

8. .Mortar made in the mortar-mill was found to be superior to that 
mixed in the usual way with a hoe. 

9. Freshwater gave better results than salt water. 

105. Adherence of Mortar. — The force with which mortars in general 
adhere to other materials depends on the nature of the material, its tex- 
ture, and the state of the surface to which the mortar is applied. 

Mortar adheres most strongly to brick, and more feebly to wood than 
to any other material. Among stones of the same class it adheres gene- 
rally better to the porous and coarse-grained than to the compact and fine- 
grained. Among surfaces it adheres more strongly to the rough than to 
the smooth. 

lot!. The adhesion of common mortar to brick and stone, for the first 
few years, is u'-e;,i er than the cohesion of its own particles. The force 
with which hydraulic cement adheres to the same materials is less than 
that of the cohesion between its own particles. 

From experiments made by Rondelet on the adhesion of common mor- 
tar to stone, it appears that it required a force varyingfrom 15 to 80 pounds 
on the square inch, applied perpendicular to the plane of the joint, to 
separate the mortar and stone after six months' union; whereas only 5 
pound- to the square inch were required to separate the same surf aces when 
applied parallel to the plane of the joint. 

THEORY ()K MORTARS. 

107. Common mortar slowly hardens in the air, from the surface towards 
the Interior, by drying and the absorption of carbonic acid. The process 
'■ Blow, but iii time, under favorable circumstances, a hard material is 
produced. The carbonic acid absorbed by the mortar combines wito the 
lime, forming a carbonate with an excess of base, and the hardening is due 
i'' this reaction and of pressure. 

108. Hydraulic mortars and paste made with hydraulic cement harden 



39 



by a species of crystallization thai takes place when the silicates of lime, 
alumina and magnesia, which are anhydrous after calcination, become 
hydrates upon being mixed with water. 

The compounds formed by burning at a high lieat the lime-stone to pro- 
duce Portland cement require but three equivalents of water for their 
hydration, while those formed at a low heat take six. This probably is 
the cause of the superior strength and hardness attained by the Portland 
cement over the quick-setting varieties. 

The presence of the silicate of magnesia in the cements obtained from 
the argillo-magnesian lime-stones is given as the reason why these cements 
are more durable for constructions in the sea, as it resists the action of sea- 
water better than the silicates of lime and alumina, unless other ingre- 
dients introduce adverse conditions. 



STUCCO, PLASTERING, ETC. 

109. The term plastering is ordinarily limited to the covering of in- 
terior walls and ceilings by coats of mortar, while that covering exterior 
walls is called stucco. This latter term was originally applied to a species 
of plastering made to resemble marble, being quite hard and capable of 
receiving a polish. Outside plastering is used often to prevent the rain 
from penetrating the joints of the masonry, and in general when it is de- 
sired to have a smooth surface instead of a rough one. 

110. In both cases, when properly done, there are three coats used, the 
first known as scratch coat, the second brown, and the third hard finish, 
or stucco. The first coat is common-lime mortar, with a given .quantity of 
bullock's hair mixed in with it. There is ordinarily a larger proportion 
of sand than in common mortar to reduce the shrinkage to a minimum. 
This, when completed and partially dry, and still soft, is scratched with a 
pointed stick in parallel scorings at right angles to each other running 
diagonally across the surface covered. When dry enough, the second or 
brown coat is applied. This differs from the first in having less hair in 
the mixture. This is followed by the third coat, hard finish for the inside, 
or stucco for the outside. The former is a paste of fine lime and plaster- 
of-Paris ; the latter is a paste of fine lime made stiff with white sand. 

If the outer plastering is to be exposed to the weather, it should be 
made of hydraulic mortar. 



40 



CONCRETES AND ARTIFICIAL STONES. 

111. Concrete is the term applied to any mixture of mortar with coarse 
materials, as gravel, pebbles, shells, or fragments of brick, tile, or stone. 

The term concrete was formerly applied to the mixture when common 
mortar was used, and beton when the mortar was hydraulic. At the pre- 
sent time these terms are synonymous, and, as a general rule, only hydraulic 
mortar is used in making them. 

A s lime or cement paste is the cementing substance in mortar, so mor- 
tar occupies a similar relation to concrete. The proportions of mortar and 
coarse materials are determined by the following principle : that the vol- 
ume of cementing substance should always be slightly in excess of the volume 
of voids in the coarse materials to be united. This excess is added as a pre- 
caution against imperfect manipulation. 

It is mixed by hand or by machinery. 

112. The process by hand is thus described : " The concrete was pre- 
pared by first spreading out the gravel on a platform of rough boards, in a 
layer from eight to twelve inches thick, the smaller pebbles at the bottom 
ami the larger on the top, and afterwards spreading the mortar over it as 
uniformly as possible. The materials were then mixed by four men, two 
with shovels ami two with hoes, the former facing each other, and always 
working from the outside of the heap to the centre, then stepping back, 
and recommencing in the same way, and continuing the operation until 
the whole mass was turned. The men with hoes worked each in conjunc- 
tion with a shoveller, and were required to rub well into tJu mortar each 
shovelful as it was turned and spread. The heap was turned over a 
Becond time, this being sufficient to make the mixture complete, covering 
tin- ciil ire surface of each pebble with mortar, and have the mass of con- 
Crete ready for use/' 

1 1:5. Various machines have been devised to effect the thorough mixing 
of the materials. The pug-mill, a cylinder in an inclined position revolv- 
ing around it- axis, a cubical box revolving eccentrically, ami various 
ol her machines, have been used. 

lit Utes of Concrete. — Concrete has been generally used iii confined 
Ituations, as foundations, or as a backing for massive walls. For manj 
it has been extensively employed in the construction of the public 
works throughout the United States, and la now extended in Its applica- 
tion, not < > 1 1 1 \ to foundations, bul even to building exterior ami partition 



4i 



walls in private buildings. It has of recent years had quite an extensive 
application in the harbor improvements in Europe. There are evidences 
of its extensive use in ancient times, many public buildings in Rome, 
palaces, theatres, aqueducts, etc. , being built of this material. It has been 
asserted that the pyramids of Egypt are built of artificial stone composed 
of small stone and mortar. 

It is especially suitable as a building material when dryness, water- 
tightness, and security against vermin are of consequence, like cellars of 
dwelling-houses, magazines on the ground or under it for storage of pro- 
visions, etc. 

115. Remarks. — To obtain uniformly a good concrete or artificial stone 
with hydraulic lime or cement, or both, it is essential — 

1. That the amount of water be just sufficient to form the cementing 
material into a viscous paste, and be systematically applied ; 

2. That each grain of sand or gravel be entirely covered with a thin 
coating of this paste ; and 

3. That the grains be brought into close and intimate contact with each 
other. 

These conditions require more than the ordinal methods and machin- 
ery used in making mortars, if a superior concrete be desired. 

116. One of the most noted for its strength, hardness, and durability, is 

BETON AGGLOMERE, OR COIGNET-BETON. 

This is the name given, to an artificial stone or concrete which has 
resulted from the experiments and researches of M. Francois Coignet, 
of Paris. 

117. Manufacture — The hydraulic lime or cement in powder, and about 
one-third its volume of water, are put into a suitable mill acting by com- 
pression and friction, and subjected to a thorough and prolonged mixing 
until a particular kind of sticky paste is obtained. The excellence of the 
beton depends greatly on this operation. If too much water be used, the 
mixture cannot be suitably rammed ; if too little, it will be deficient in 
strength. 

The sand, deprived of its surplus moisture, and the paste, in suitable 
proportions, are put in a powerful mill, and subjected to a thorough mixing 
until the compound presents the proper appearance, which is that of a 
pasty powder. 



42 



Tii ■ proportions will vary according to the probable uses of the stone ; 
of sand lo 1 of hydraulic lirne in powder, by volume, and 5 of sand, 1 of 
hydraulic lime, and 1 of Portland cement, are sometimes used. The 
materials, being in a state of pasty»powder, are now ready to be placed in 
moulds. Each grain of sand being coated with the paste, it is now essen- 
tial that they Ik- brought in intimate contact with each other. 

This is effected by placing the paste in layers of 1£ to 2 inches thick 
in strong moulds capable of sustaining a heavy pressure, and ramming 
each layer as it is placed by repeated blows of an iron-shod rammer 
until the stratum of material is reduced to about one-third of its original 
thickness. The upper surface is struck with a straight-edge and smoothed 
off with a trowel. The mould is turned over on a bed of sand, and de- 
tached from the block. If it be a small one, it may be handled after one 
day ; larger pieces should have longer time to harden. 

This stone has had quite an extensive application in France ; aque- 
ducts, bridges, sewers, cellars of barracks, etc., have all been built with it. 

kansome's patent stone. 

118. Among other artificial stones that are offered to the builder are 
several bearing the name of Ransome, an English engineer. The patent 
silicious stone, Ransome's apcenite, and Ransome's patent stone, are all 
artificial sand-stones, in which the cement is a silicate of lime. They 
differ mostly in the process of making. The patent stone has been made 
in S:ui Francisco and in Chicago, and employed to some extent in those 
cities. 

11!). Dry sand and a solution of silicate of soda, about a gallon of the 
silicate to the bushel of sand, are thoroughly mixed in a proper kind of 
mill, and then moulded into any of the tonus required. These blocks or 
forma are then saturated by ;i concentrated solution of calcium chloride, 
which i- forced through the moulded mass by exhaustion of the air, by 
gravity, or Other suitable means. The reactions of the agents result in an 
insoluble silicate of lime, which firmly unites all the grains of the mass 
Into one -olid, ami n solution of sodium chloride (common salt). The 
latter la removed bj washing with water. 

Tin- artificial atone* thUfl formed i> uniform ami homogeneous in its 
texture, and said to be tree from liability to distortion or shrinkage. It is 
claimed that it i-* nol affected i»\ variations o\' climate or temperature. 



43 



120. Mastics is the term generally applied to artificial or natural com- 
binations of bituminous or resinous substances with other ingredients. 

They are used as cements for other materials, or as coatings to render 
them water-proof. 

121. Artificial mastics have been formed by mixing coal-tar, vegetable 
tar, pitch, etc., with powdered lime-stone, powdered brick, litharge, etc., 
but they are inferior to those obtained by using bituminous lime-stone 
reduced to a powder, mixed with asphaltum, and known as bituminous 
mastic. 

122. Bituminous mastic is prepared by heating the mineral pitch or 
asphaltum in a large caldron or iron pot, and stirring in the proper pro- 
portion of the powdered lime- stone. This operation, although very 
simple in its kind, requires great attention and skill on the part of the 
workmen in managing the fire, as the mastic may be injured by too low 
or too high a degree of heat. The best plan appears to be to apply a brisk 
fire until the boiling liquid commences to give out a thin, whitish vapor. 
The fire is then moderated and kept at a uniform state, and the powdered 
stone is gradually added, and mixed in with the tar by stirring the two 
well together. When the temperature has been raised too high, the heated 
mass gives out a yellowish or brownish vapor. In this state it should be 
stirred rapidly, and be removed at once from the fire. 

When the mixing is completed the liquid mass is run into moulds, 
where it hardens into blocks of convenient shape and size. 

The stone used is a carbonate of lime naturally impregnated with 
bitumen, called sometimes Seyssel asphalt, from the place where it was 
quarried. The proportion in the Seyssel stone is oftentimes as much as 
83 of calcareous matter to IT of bitumen, and the amalgamation is more 
perfect than that of any artificial compound of the kind yet invented. 
To prepare it for the operation just described, the stone may be reduced 
to powder either by roasting it in vessels over a fire, or by grinding it 
down in the ordinary mortar-mill. For roasting, the stone is first reduced 
to fragments the size of an egg. These fragments are put into an iron 
vessel, heat is applied, and the stone is reduced to powder by stirring it 
and breaking it up with an iron instrument. This process is not only less 
economical than grinding, but the material loses a portion of the bitumen 
from evaporation, besides being liable to injury from too great a degree 



44 



of heat. For grinding, the stone is first broken as for roasting. Care 
should be taken, during the process, to stir the mass frequently, otherwise 
it may cake. 

123. To use the mastic, the blocks are remelted, and the mixture is laid 
on the surface to be coated by pouring it on generally in squares or thin 
blocks, care being taken to form a perfect union between the edges, and 
rubbing the surface smooth with an ordinary wooden float, especially if it 
is to receive another layer. 

Or, having melted the mastic, mixing it with sand, and applying to the 
surface to be coated. Supposing it to be used for a floor, it is applied as 
follows : 

The mastic is broken into small pieces, not more than half a pound 
each, and placed in a caldron or iron pot over a fire. It is constantly 
stirred to prevent burning, and as soon as melted two parts of sand to one 
of mastic are gradually added, and the whole mass constantly stirred until 
the mixture will drop freely from the implement used in stirring. 

The ground having been made perfectly firm and smooth, covered with 
concrete, or otherwise prepared, the mixture is applied as in the previous 
case, and the surface smoothed with the float. Before it becomes hard a 
small quantity of fine sand is sifted over it and well rubbed in with a 
trowel or hand-rloat. 

The thickness of the coating will depend upon its situation, being less 
for the capping of an arch than for the flooring of a room, and this less 
than a hall or pavement where many are passing. 

124. The term asphalt is sometimes employed to designate the bitumi- 
nous lime-stone, more generally the mastic after it has been moulded into 
blocks tor transportation, frequently to the product obtained by mixing 
sand with the mastic, and by mineralogists often to the raw bitumen or 
mineral tar. Calling the first asphalt, the other two would be respectively 
asphaltic mastic and asphaltic concrete. 

L2Q. Proportions.— It is usually mixed at about 1 part of asphaltum to 
I OF 8 by measure of the powdered lime-stone, according as the stone con- 
tains more or less bitumen. 

If petroleum or naphtha be presenl in the stone, it must be removed. 
*hich U gem rallj dene bj distillation, clay in the lime-stone injures the 
mastic, and Is oftentimes the cause of the cracks seen in the asphaltic con- 
i pete after it has been laid 

L96 Asphaltum alone has been frequently used for coatings, but in time 



45 



it becomes dry and peels off. But made into the mastic, the evaporation is 
prevented and its durability increased. 

The impurities and volatile ingredients of coal-tar, mineral tar, and 
similar substances render them less durable than the mineral pitch, and the 
combinations made with them are inferior to those made with the latter, 
as might be expected. But for certain purposes they are extremely useful, 
as they possess in a measure the advantages of the other, and are quite 
cheap. 

127. Uses. — The combinations of asphaltum were well known to the 
ancients, and a cement made of it is said to have been employed in the 
construction of the w T alls of Babylon. 

The principal uses of the mastic at the present day are for paving 
streets, sidewalks, floors, cellars, etc., and forming water-tight coatings for 
cisterns, cappings of arches, terraces, and other similar roofings. 

It has quite an extensive use in Europe at the present time. The prin- 
cipal sources of the asphalt are from the Jurassic range in the Val de 
Travers, at Pyrimont, near Seyssel on the Rhone, and the neighboring- 
localities, and Bechelbronn (or Lobsan), in Alsace. 



CHAPTEE IV. 

BRICK. 

128. Brick may be considered an artificial stone made by moulding 
wed clay into forms of the requisite shape and size, and hardening 

them either by baking in the sun or burning in kilns, or other contrivances. 
When hardened by the first process, they are known as sun-dried, and by 
the latter as burnt brick, or simply brick. 

129. Sun-dried bricks have been in use from the remotest antiquity, 
beiug found in the ruins of ancient Babylon. They were used by the 
Greeks and Romans, and especially by the Egyptians. 

They were ordinarily made in the spring or autumn, as they dried 
more uniformly during those seasons, while those made in the summer, 
drying too rapidly on the exterior, were apt to crack upon further drying 
in the interior. 



4tf 



Tt was customary not to use them until two years after they had been 
made. 

At present they arc seldom employed. 

Walls made of earth hardened in a similar way, known as adobes, are 
found in parts of our country and in Mexico. They form a simple and 
economical mode of construction where the weights to be supported are 
moderate, and fuel is very scarce and expensive. This mode, however 
suitable for ;; southern climate, is not fit for our north. 

130. Brick when properly burnt acquires a degree of hardness and 
durability that renders it suitable for nearly all the purposes to which stone 
is applicable ; for, when carefully made, its strength, hardness, and dura- 
bility are but little inferior to the ordinary kinds of building-stone. It 
remains unchanged under the extremes of temperature, resists the action 
of water, sets firmly and promptly with mortar, and, being both cheaper 
and lighter than stone, is preferable to it for many kinds of structures, as 
arches, the walls of houses, etc. 

The Romans employed this kind in the greater part of their construc- 
tions. The scarcity of stone in Holland and the Netherlands led to the 
extensive use of this material not only in private but in their public build- 
ings, and these countries abound in fine specimens of brick-work. 

181. Brick-making was introduced into England by the Romans, and 
arrived at great perfection during the reign of Henry VIII. 

The art of brick-making is now a distinct branch of the useful arts, 
and the number annually made in this country is very great, amounting to 
thousands of millions. 

132. Good bricks should be free from cracks and flaws, hard, possess a 
regular form, uniform size, and, where exposed to great heat, infusibility. 

These qualities depend upon a proper selection of the brick-earth, its 
preparation, and it>- manufacture into brick. 

L38. The argillaceous earths suitable for this purpose may be divided 
into three principal classes, viz. : 

/'///-, days, those eomposcd chiefly of aluminum silicate, or one part 
of alumina and two of silica, combined with a small proportion of other 
substances, as lime, soda, magnesia, ferrous oxide, etc.; 

Loams, v, hicll are mechanical mixtures o\' clay and sand ; and 

W 'Is, w hicll are mechanical mixtures of clay and carbonate of lime. 

184. Pure clay, being made plastic with water, may be moulded into any 

shape, inn will shrink and crack in drying, however carefully and slowly 



47 



the operation be conducted. By mixing a given quantity of sand with it 
these defects may be greatly remedied, while the plastic quality of the clay 
will not be materially affected. 

The loams oftentimes have too much sand, and are then so loose as to 
require an addition of clay or other plastic material to bind them together. 

135. Earth containing the proper proportions of clay and sand suitable 
for making brick is frequently found, but, if it be not naturally fit for the 
purpose, it should be made so by adding that element which is necessary. 
The proportion of sand or clay to be added should be determined by direct 
experiments. 

Silicate of lime in any considerable quantity in the earth makes it too 
fusible. Carbonate of lime, being converted into lime during the burning, 
which absorbs moisture upon being exposed, would cause disintegration in 
the brick if present in any considerable quantity. 

136. The earth being of the proper kind, the first thing is to dig it out 
before the cold weather, and carry it to a place prepared to receive it. It 
is there piled into heaps and exposed to the weather during the winter, to 
be mellowed by the frosts, which break up and crumble the lumps. 

In the spring the earth is turned over with shovels, the stones, pebbles, 
and gravel removed, and the necessary amount of clay or sand added, if 
either be wanting. It is then tempered either by hand or by machinery. 

The object of tempering is to bring the earth into a homogeneous paste 
for the use of the moulder. This is effected by mixing it with about half 
its volume of water, and stirring it and kneading it, either by turning it over 
repeatedly with shovels, and treading it over by horses or men until the 
required plasticity is obtained, or by using the pug-mill or similar ma- 
chine. 

The plastic mass is then moulded into the proper forms by hand or 
machinery. 

137. When made by hand, the mould used is a kind of box without top 
or bottom, and the process consists in dashing the tempered clay into it 
with sufficient force to completely fill it, and removing the superfluous clay 
by striking it with a straight-edge. The newly-made brick is then turned 
out on a drying-floor to harden, or on a board, and carried to the place 
where it is to dry. 

138. Bricks are now generally moulded by machines. These combine 
the pug-mill with an apparatus for moulding, receiving the clay as dis- 
charged from the pug-mill, pressing it in moulds, and pushing the brick out 



48 



in front, where they are removed from the frames and carried to the dry- 
ing-floor. 

139. Drying. — Great attention is necessary in this part of the process of 
manufacture. They are dried in the open air or in a drying-house, being 
spread out on the ground or floor, and frequently turned over until they 
are sufficiently hard to handle without injury. They are then piled into 
stacks under cover for further drying. 

The main points to be observed in drying are to protect them from the 
direct action of the sun, from draughts of air, rain, and frost, and to have 
each brick dry uniformly from the exterior inwards. The time allowed for 
drying depends upon the climate, the season of the year, and the weather. 

140. Burning. — The next stage of their manufacture is the burning. 
The bricks are arranged in the kiln so as to allow the passage of the heat 
around them, which is effected by piling the bricks so that a space is left 
around each brick. This arrangement of the bricks is so made as to allow 
the heat to be diffused equally throughout, to afford a good draught, and 
to keep up a steady heat with the least amount of fuel, and is called setting 
the kiln. 

A very moderate fire is then applied under the arches of the kiln to 
expel any remaining moisture from the raw brick ; this is known to be 
completely effected when the smoke from the kiln is no longer black. The 
tire is then increased until the bricks of the arches attain a white heat ; it 
is then allowed to abate in some degree, in order to prevent complete 
vitrification ; and it is alternately raised and lowered in this way until the 
burning is complete, which may be ascertained by examining the bricks at 
the top of the kiln. The cooling should be slowly effected ; otherwise the 
bricks will not withstand the effects of the weather. It is done by closing 
the mouths of the arches and the top and sides of the kiln in the mosl 
effectual manner with moist clay and burnt brick, and allowing the kiln to 
remain in this state until the heat has subsided. The length of time of 
burning varies, but fifteen days or thereabouts is not unusual. 

ill. From the nature of this process it will be evident that bricks of 
very different qualities must be found in the same kiln. There will be at 
least three varieties: I, ibose burned too much; 0, those just enough; 
and, o, those not enough. The bricks forming the arches and adjacent to 
them, being Dearer the fire, will be burnt to great hardness, or perhaps 
vitrified; ibose in (he interior will be well burnt; and those mi top and 
near I be exterior will be under burned. The fust are called arch brick, the 



49 



second body, hard, and, if ferrous-oxide was present in the clay, cherry 
red, and the third soft, pale, or sammel brick. 

The arch bricks are very hard, bat brittle, and set badly with mortar ; 
the soft or sammel, if exposed to the weather, have neither strength nor 
durability, and therefore can only be used for inside work. 

142. Size. — The size and form of bricks vary but little. They are 
generally rectangular parallelopipedons, about 9 inches long, 4^ inches 
broad, and 3 inches thick, the exact size varying with the contraction of 
the clay. 

143. Bricks are generally divided into two kinds, common and pressed.' 
The latter were made by putting the raw bricks, when nearly dry, into 
moulds of proper shape, and submitting them to a heavy pressure by 
machinery. These were baked rather than burned, and heavier than the 
common brick. The machine-made bricks partake of the nature of 
pressed brick. 

144. Characteristics of good bricks : 

They should be regular in shape, with plane, parallel surfaces and 
sharp, right-angled edges ; 

Give a clear, ringing sound when struck ; 

When broken across, show a fine, compact, uniform texture, free from 
air-bubbles and cracks ; and 

Not absorb more than -fe of their weight of water. 

145. Fire-bricks are made of refractory clay containing no lime or 
alkaline matter which remains unchanged by a degree of heat that would 
vitrify and destroy common brick. They are baked rather than burnt, and 
their quality depends upon the fineness to which the clay has been ground 
and the degree of heat used in making them. 

They are used for facing fire-places, lining furnaces, and wherever a 
high degree of temperature is to be sustained. 

146. Bricks light enough to float in water were known to the ancients. 
During the latter part of the last century M. Fabbroni, of Italy, succeeded 
in making floating bricks of a material known as agaric mineral, a kind of 
calcareous tufa, called fossil meal. Its weight was only one-sixth that of 
common brick ; it was not affected by the highest temperature, and was 
a bad conductor of heat. 

147. Tiles. — They are divided into three classes, roofing, pacing, and 
draining tiles. 



50 



Their manufacture is very similar to that of brick, the principal dif- 
ferences arising from their thinness. This requires the clay to be stronger 
and purer, and greater care taken in their manufacture. 

Their names explain their uses. 



CHAPTEE V. 



WOOD. 

148. The abundance and cheapness of this material in the United States, 
the ease with which it could be procured and worked, and its strength, 
lightness, and durability, under favorable circumstances, have caused its 
very general use in every class of constructions. 

149. Timber, from the Saxon word timbrian, to build, is the term ap- 
plied to the wood of a suitable size for building purposes. While in the 
tree it is called standing timber ; after the tree is felled, and the portions fit 
for building are cut into proper lengths, these are called logs or rough 
timber ; when these have been squared or cut into shape, either to be used 
in this form or cut into smaller pieces, if from the trunk of the tree, the 
term timber is applied, and known as square or round, hewn or sawed, ac- 
cording to the form of cross-section and mode of cutting it ; if of crooked 
shape from the branches or roots, compass timber. The latter is used in 
ship-building. 

The logs, being sawed into smaller pieces, form Inmln r, and this is 
divided into classes known as joists, scantlings, strips, boards, planks, etc., 
and, when sawed to suit a given bill, dimension stuff. 

150. The trees used for timber are exogenous — that is, they grow or in- 
crease iii size by formation of new wood in layers on its outer surface. 

The trunk of a full -grown tree presents three distinct parts : the bark t 
which forms the exterior coating ; (hemp Wood, which is next to the bark ; 
the heart, or Inner part, which is easily distinguishable from the sap-wood 



51 



by its greater density, hardness, and strength, and oftentimes by its darker 
color. 

151. The heart forms the essential part of the trunk as a building ma- 
terial. The sap-wood possesses but little strength, and is subject to rapid 
decay, owing to the great quantity of fermentable matter contained in it ; 
and the bark is not only without strength, but, if suffered to remain on 
the tree after it is felled, it hastens the decay of the sap-wood and 
heart. 

152. Trees should not be felled for timber until they have attained 
their mature growth, nor after they exhibit symptoms of decline ; other- 
wise the timber will be less strong and far less durable. Most forest trees 
arrive at maturitj^ between fiftj^ and one hundred years, and commence to 
decline after one hundred and fifty or two hundred years. The age of the 
tree can, in most cases, be ascertained either by its external appearances 
or by cutting into the centre of the trunk, and counting the rings or 
layers of the sap and heart, as a new ring is formed each year in the pro- 
cess of vegetation. When the tree commences to decline, the extremities 
of the old branches, and particularly the top, exhibit signs of decay. 

153. Trees should not be felled while the sap is in circulation ; for this 
substance is of a peculiarly fermentable nature, which, remaining in the 
timber, is very productive of destruction of the wood. The best author- 
ities on this subject agree that the tree should be felled in the winter 
season. 

154. This is the practice in the United States, not so much on account 
of the sap not being in circulation, as for the reason that the winter season 
is the best for procuring the necessary labor, and is the most favorable 
time for moving the logs from where they are cut to the points where the} r 
are to be made into rafts. 

155. Appearances of good timber. — In the same species, that one will in 
general be the strongest and most durable which has grown the slowest, 
as shown by the narrowness of the annual rings. 

And generally the heaviest one of the same species will possess these 
qualities with respect to the others. 

The grain should be hard and compact, and, if the wood has a color, 
the darker it is, the stronger will it be as a rule. 

If a cut be made in it, the fresh surface of the cut should be firm and 
shining;. 



52 



It should be free from all blemishes and defects. 
It should be straight-grained and free from knots. 

156. Defects. — These arise from some peculiarity in the growth of the 
tree or from the effects of the weather. 

Strong winds oftentimes injure the growing tree by twisting or bend- 
ing it so as to partially separate one annual layer from another, forming 
what is known as rolled timber or shakes. 

Severe frosts cause sometimes cracks radiating from the centre to the 
surface. 

These defects, as well as those arising from worms or age, may be seen 
by examining a cross-section of the log. 

157. Glasses. — For use in construction timber is divided into two gen- 
eral classes, soft icood and hard wood. 

The first includes all coniferous trees like the pines ; and the other 
all the timber trees that are non-coniferous, like the oaks, etc. 

The first class in general contains turpentine, and is distinguished by 
straightness of fibre and regularity of form. It is more easily sawed or 
split along the grain, and much more easily broken across the grain, than 
the second class. 

The hard-wood or non-coniferous timber has no turpentine, and, as a 
class, is tough and strong. 

158. Seasoning. — Timber is said to be seasoned when by some process, 
either natural or artificial, the moisture in it has been expelled so far as to 
prevent decay from internal causes. 

By seasoning, drying so as to expel the water of the sap is not only 
meant, but also a removal or change of the albuminous substances. These 
are fermentable, and, when present in the timber, are ever ready, under 
suitable circumstances, to promote decay. 

The seasoning of timber is of the greatest importance, not only to its 
durability, bul to the solidity of the structure for which it maybe used ; 
;i- shrinking of some of the pieces, arising from the seasoning oi the 
wood. |f used while green, might, in many cases, cause material injury. 
If not complete destruction, to the structure. 

159. Natural Seasoning consists in exposing the timber freely to the air 
in B dry place, sheltered, if possible, from the sun and high winds 

li is preferable to any other, as timber seasoned in this way is both 
itronger and more durable than when prepared by any artificial process. 



53 



Most timber will require, on an average, about two years io become fully 
seasoned ln T this method. 

As this takes a long time, artificial methods are used to effect it more 
rapidly. 

160. Water Seasoning, the simplest of these, consists in immersing the 
timber in water as soon as cut, care being taken to keep it entirely sub- 
merged, and, after a fortnight's soaking, removing it to a suitable place and 
drying it. If the timber is full of sap when immersed, the water will re- 
move the greater portion of it, This method doubtless weakens the tim- 
ber to some extent, and is therefore not recommended where strength in 
the timber is of material importance. 

161. Boiling and Steaming have both been used, but are open to the 
same objection as the last, by impairing the elasticity and strength of the 
timber. 

162. Hot-air Process. — This consists in exposing the timber in a chamber 
or oven to a current of hot air, the temperature varying according to the 
kind and size of the timber to be seasoned. This is considered the best of 
the artificial methods. The time required depends upon the thickness of 
the timber to be seasoned, ordinary lumber requiring from one to ten 
weeks to season sufficiently. 

163. Durability and Decay of Timber. — Timber lasts best when kept or 
used in a dry and well-ventilated place. Its durability depends upon its 
protection from decay and the attacks of worms and insects. 

The icet and dry rot are the most serious causes of the decay of tim- 
ber. 

164. Wet Rot is slow combustion, a decomposition of moist organic 
matter exposed to the air, by the oxygen of which it is gradually burned 
and destroyed without sensible elevation of temperature. The decay from 
wet rot takes place only by contact, and requires the presence of mois- 
ture. 

To guard against it, the timber must not be subjected to a condition of 
alternate wetness and dryness, or even a slight degree of moisture, if 
accompanied by heat and Confined air. 

165. Dry Rot is a disease in timber arising from the decomposition of 
the albumen and other fermentable substances, accompanied by the growth 
of a fungus, whose germs are easily carried in all directions, when it makes 
its appearance, without actual contact being necessary, which finally 



54 



converts the wood into a fine powder. The fungus is not the cause of 
decay ; it only converts corrupt matter into new forms of life. 

Timber not properly seasoned, used where there is a want of free circu- 
lation of air, even if there be only a small amount of moisture present, 
or covered while in this state by a coat of paint or similar substance pre- 
venting its drying, decays by this disease. 

Slaked lime hastens the decay of timber, which should therefore in 
buildings be protected against contact with the mortar. 

166. Timber immersed in salt water is liable to the attacks of two of 
the destructive inhabitants of our waters, the Limnoria terebrans and 
Teredo n avails, the former of which rapidly destroys the heaviest logs by 
gradually eating in between the annual rings, and the latter, the well- 
known ship-worm, by converting timber into a perfectly honeycombed state 
by its numerous perforations. 

DURABILITY UNDER CERTAIN CONDITIONS, AND MEANS OF INCREASING IT. 

167. Timber may be subjected to the following conditions : 
It may be kept constantly dry, at least practically ; 

It may be kept eon stantly wet in fresh water ; 

It may be constantly damp ; 

It may be alternately wet and dry ; 

It may be eon stonily wet in sea-water. 

168. Timber kept constantly dry will last for centuries. 

The roof of Westminster Hall is more than 450 years old. In Stirling 
Castle arc carvings in oak, well preserved, over 300 years old; and the 
trusses of the roof of the Basilica of St. Paul, Rome, were sound and good. 
after 1,000 years of service. The timber dome of St. Mark, at Venice, was 
in good .condition 850 years after it was built. 

Under this condition it would seem hardly worth while to attempt to 
increase its durability, except where it may be necessary to guard against 
the attacks of insects, which are very destructive in some climates. 

16 ( .>. Timber kept constantly met in fresh water under such conditions as 
l<» exclude the air is also very durable. 

Beneath the foundation of Savoy Place, London, oak, elm, beach, and 
chestnut piles and planks were found in a perfect state of preservation 

after hai Ing been there 650 years. 



55 



The piles of the old London Bridge were sound 800 years after they 
were driven. The piles of the bridge built by Trajan, after having been 
driven more than 1,600 years, were found to have a hard exterior, similar 
to a petrifaction, for about four inches, and the rest of the wood to be in 
its ordinary condition. 

We may conclude that timber submerged in fresh water would need no 
artificial aid to increase its durability, although in a measure it would be 
softened and weakened. 

170. Timber in Damp Situations. — Under these circumstances timber is 
in a place very unfavorable for its durability, and is liable, as previously 
stated, to decay rapidly. In such situations only the most durable kind is 
to be employed, and every precaution should be taken to increase its 
durability. 

171. There are three conditions which are at our command for in- 
creasing the durability of timber in damp situations : 

1st. Thoroughly season it; 

2d. Keep a constant circulation of air about it ; and 

3d. Cover it with paint, varnish, or pitch. 

The first condition is essential, and may be combined with either or 
both of the others. 

The cellulose matter of the woody fibre is very durable when not acted 
upon by fermentation, and the object of seasoning is to remove or change the 
fermentable substances, as well as to expel the moisture in the timber, 
thus protecting the cellulose portion from decay. Even if it be well 
seasoned, thorough ventilation is indispensable in such situations. 

The rapid decomposition of sills, sleepers, and lower floors is not sur- 
prising where neither wall-gratings nor ventilating flues carry off the 
moisture rising from the earth or foul gases evolved in the decay of the 
surface-mould. 

If we remove the earth to the bottom of the foundation, and fill in the 
cavity with dry sand, plaster-rubbish, etc., etc., or lay down a thick 
stratum of cement or concrete to exclude the water, and provide for a com- 
plete circulation of air, the lower floors will last nearly as long as the 
upper ones. 

172. While an external application of paint, or pitch, or oil laid on hot 
increases the durability of well-seasoned timber, nothing can more rapidly 
hasten decay than such a coating upon the surface of unseasoned or green 



56 



timber. This mistake is daily made, and dry rot inevitably follows. The 
coating of paint closes the pores of the outer surface, and prevents the 
escape of the moisture from within, thus retaining in the wood the 
elements of decay. 

178. Timht r alternately Wet and Dry. — The surface of all timber exposed 
to alternations of wetness and dryness gradually wastes away, becoming 
dark-colored or black. This is wet rot, or simply " rot" 

Density and resinousness exclude moisture to a great extent ; hence 
timber possessing these qualities should be used in such situations. Heart- 
wood, from its superior density, is more durable than sap-wood ; oak, than 
poplar or willow. Resinous wood, like the Southern pine, is more durable 
than ash or beech, etc. 

174. Timber constantly Wet in Sea- Water. — The remarks made about 
timber placed in fresh water apply to this case. Those parts, however, 
standing between half-ebb and half-flood tides are peculiarly liable to 
attacks from the mollusks, Toredo navalis, and Limnoria terebrans. The 
timber, from at least the level of lowest tide to the highest, and, according 
to many, from the bottom, should be protected from them, which is done 
by sheathing it with copper, or thickly studding the surface with broad- 
headed iron nails, or other similar device. Resinous woods resist their 
attacks longer, which is most probably due to the resin in the wood. 
This is after a time washed or dissolved out, and the timber is speedily 
destroyed by them. Saturation of the timber with dead oil by the process 
known as creosoting seems to act as a preservative to the timber in this 
case. 

PRESERVATION OE TIMBER. 

1?."). The necessity of putting timber in damp places, or where 
it will be exposed to alternate wetness and dryness, has caused nu- 
merous experiments to be made to increase its durability under such 
circumstances by preventing or delaying its decay. 

There are many patented processes having this object in view, 
which are based either on the principle of expelling the albuminous 
Substances, and replacing them by others of a durable nature, or by 

changing the albuminous substances into insoluble compounds i>\ saturat- 
ing the timber with Baits of an eaithv or metallic base which will 



51 



combine with them. Some of those which have been proposed or used 
are as follows : 

176. Kyanizing. — Kyan's process is to saturate the timber with a 
solution of chloride of mercury, one pound of the chloride to four gallons 
of water. 

Long immersion in the liquid in open vats, or great pressure upon 
both solution and wood in large wrought-iron tanks, is necessary for 
the complete injection of the liquid. 

The expensiveness of the process and its unhealthiness to those em- 
ployed in it forbid its extensive use. 

177. Burnettizinr/. — Burnett's process is to use a solution of chloride of 
zinc, one pound of the chloride to ten gallons of water, which is forced 
into the wood under a pressure of 150 pounds to the square inch. 

178. Earle's process consists in boiling the timber in a solution of one 
part of sulphate of copper, three parts of the sulphate of iron, and one 
gallon of water to every pound of the salts. A hole was bored the whole 
length of the piece before it was boiled. It was boiled from two to four 
hours, and allowed to cool in the mixture. 

171). Ringold and Earle invented the following process : A hole was 
made the whole length of the piece, from \ to 2 inches in diameter, and 
boiled from two to four hours in lime-water. After this piece was dried 
the hole was filled with lime and coal-tar. Neither of these methods was 
very successful. 

180. A Mr. Darwin suggests that the piece be soaked in limewater, and 
afterwards in sulphuric acid, so as to form gypsum in the pores. 

181. Mr. S. Beer, of New York City, invented a mode of preserving 
timber bj boiling it in borax with water. But this process has been 
objected to, on the ground that it is not a good protection against 
moisture. 

Common salt is known to be a good preservative in many cases. 
According to Mr. Bates's opinion it answers a good purpose in many cases 
if the pieces to which it is exposed are not too large. 

182. B<> a cli eric, employed a solution of sulphate of copper or pyrolig- 
nite of iron. He enclosed one end of the green stick in a close-fitting 
collar, to which is attached a water-tight bag communicating through a 
flexible tube with an elevated reservoir containing the solution. Hydro- 
static pressure soon expels the sap at the opposite end of the log. When the 
solution issues in a pure state from the opposite end, the process is complete. 



f>8 



He finds the fluid will pass along the grain a distance of twelve feet 
under less pressure than is necessary to force it across the grain three- 
fourths of an inch. The operation is performed upon green timber with 
the greatest facility. 

In 1840, 80,000 sleepers of the most perishable woods, impregnated, by 
Boucherie's process, with sulphate of copper, were laid down on French 
railways. After nine years' exposure they were found as perfect as when 
.laid. This experiment was so satisfactory that most of the railways of that 
country at once adopted the system. It has been suggested to wash out 
the sap with water, which would not coagulate its albumen, and then use 
the solution. 

183. Bethel's process. — This consists in placing the timber in an air-tight 
cylinder of boiler-iron, and partially exhausting the air. Dead oil is then 
admitted at a temperature of 120° Fahr., and a pressure of about 150 
pounds to the square inch is then applied, which is maintained from five 
to eight hours, according to the size of the timbers under treatment. The 
oil is drawn oft* and the timber removed. 

184. The Seely process consists in subjecting the wood while immersed 
in dead oil to a temperature between 212° and 300° Fahr. for a sufficient 
length of time to expel any moisture present, The water being expelled, 
the hot is quickly replaced by cold oil, by means of which change the 
steam in the pores of the timber is condensed, a vacuum formed, into which 
oil is forced by atmospheric pressure and capillary attraction. From six 
to twelve pounds of oil to the cubic foot of wood is expended in the 
process. 

The theory is that the first part of the operation seasons the wood, de- 
stroying or coagulating the albumen, and expelling the moisture ; and the 
second part tills the wood-cells with a material that is an antiseptic, resist- 
ing destructive agents of every kind. 

185. Robbings process consists in treating timber with coal-tar in the 
form of vapor. 

The most approved of these methods is that known as Sedtfs, which is 
:i modification and an improvement of Bethel's process, and is generally 

know n as " m OWting." 

188 The following are the names of the inventors and the material 
used by them in the different processes that have from time to time been 
in forward tor the purpose <>t preserving timher: 



59 



Names. 


Chemicals used. 


Manner of 
using them. 


Bethel. 


Creosote, pitch, or dead oil. 


By injection. 


Seely. 


" 


" 


Robbins. 


(( U (< 


a (( 


Kyan. 


Chloride of mercury. 


(< (< 


Margary. 


Sulphate of copper. 


" " 


Burnett. 


Chloride of zinc. 


" " 


Ransome. 


Liquid silicate of potassa. 


(( (« 


Le Gras. 


Manganese, lime, and creosote. 


" " 


Margary. 


Solution of acetate of copper. 


a a 


Payne. 


Sulphate of iron, carbonate of soda. 


" " 


Boucherie. 


Pyrolignite of iron or sulphate of copper. 


" " 


Gemini. 


Tar. 


(< (< 


Heinmann. 


Resin or colophony. 


(( (< 


Earle. 


Sulphate of copper. 


' ' boiling. 


RlNGOLD. 


Lime. 


" " 


Tregold. 


Sulphate of iron. 


(( it 


S. Beer. 


Borax. 


a a 


Dorset and 


Same as Boucherie. 


By means of a vac- 


Blythe, 




uum and injec- 
tion. 


HUTING AND 


Oil of schist, tar, pitch, and shellac. 


By immersion, and 


Boutigny. 




by fire or burn- 


Vernet. 


Arsenic. 


ing. 
By saturation. 


Bates. 


Salt. 


External applica- 






tion. 



It is thought that the ancient Egyptians knew of some process of pre- 
serving wood. Old cases, supposed to have been 2,000 years old, apparent- 
ly of sycamore impregnated with bitumen, have been found perfectly sound 
and stroiis;. 



KINDS OF TIMBER-TREES IN THE UNITED STATES. 

187. The forests of our own country produce a great variety of the best 
timber for every purpose, and supply abundantly both our own and foreign 
markets. The following are some of the examples in most common use. 

Examples of the soft woods : 

Yellow Pine (Pinus variabilis). — The heart-wood of this tree is fine- 
grained, moderately resinous, strong, and durable ; but the sap-wood is 
very inferior, decaying rapidly on exposure to the weather. The timber 
is in very general use for frame-work, etc. 

This tree is found throughout our country, but in the greatest abun- 
dance in the Middle States. In the Southern States it is known as Spruce 
Pine and Short-leaved Pine. 



60 



Long-kneed Pine, or Southern Pine {Pinus palustris).— This tree has 
but little sap-wood ; and the resinous matter is uniformly distributed 
throughout the heart-wood, which presents a fine compact grain, having 
more hardness, strength, and durability than any other species of the 
pine, owing to which qualities the timber is in very great demand. 

The tree is first met with near Norfolk, Virginia, and from this point 
south it is abundantly found. 

White Pine, or Northern Pine {Pinus strobu^—This tree takes its 
name from the color of its wood, which is white, soft, light, straight- 
grained, and durable. It is inferior in strength to the species just de- 
scribed, and has, moreover, the defect of swelling in damp weather. Its 
timber is, however, in great demand as a good building material, being ex- 
tensively used throughout the Eastern and Northern States. It is found 
between the 43d and 47th parallels of north latitude, the finest specimens 
being found in Maine. 

188. Nonoay Pine {Pinus rabra.) — This is a species found in the North- 
west, especially in Michigan and Wisconsin, where it ranks very high, 
comparing favorably with the common yellow pine, although having less 
resin in it. 

189. The genus Fir {Abies) furnish large quantities of good timber and 
lumber, which are extensively used throughout the North. The common 
fir {Abies alba and Abies nigra), the spruce fir, found in Northern Califor- 
nia, and the Oregon fir [Pinus {Abies) Douglasii], which grows to an enor- 
mous size, all furnish good building material. 

190. Hemlock {Allies Canadensis) is a well-known species that is used 
throughout the Northern States for planking floors of every kind, and a 
substitute for pine when this is difficult or expensive to procure. It is 
very perishable in moist situations or when subjected to alternate wetness 
and dryness. It has been used in considerable quantities on the Lakes in 
improvements where ii is entirely submerged in fresh water. Hemlock 
timber is often shaky, and splits more easily than pine. 

191. The Juniper or White Oedar and the Cypress arc- very celebrated 
lor affording a material whieh is very light and of great durability when 
exposed to the weather; owing to these qualities, it is almost exclusively 
used for shingles and other exterior coverings, These two trees are Pound 

in greal abundance in the swamps of the Southern Slates. 

192. The foregoing kinds of timber, especially the pines, are regarded 

tluable building materials, owing to their strength and durability, the 



61 



straightness of the fibre, the ease with which they are worked, and their 
applicability to almost all the purposes of constructions in wood. 



EXAMPLES OF HARD-WOOD TIMBER TKEES. 

19o. Whtti Oak (Quercus alba).— The bark of this tree is light, nearly 
white : the leaf long, narrow, and deeply indented ; the wood compact, 
tough, and pliable, of a straw color with a pinkish tinge. 

It is largely used in ship-building, the trunk furnishing the necessan- 
timber for the heavy frame-work, and the roots and large branches afford- 
ing an excellent quality of compass-timber. Boards made from it are lia- 
ble to warp and crack. This tree grows throughout the United States and 
Canada, but most abundantly in the Middle States. Its proximity to salt 
air during the growth of the tree appears to improve the quality of the 
timber. The character of the soil has a decided effect on it. If grown in 
a moist soil, the tree acquires a larger size, but the timber is less firm and 
decays sooner. 

194. Live Oak (Quercus virens). — The wood of this tree is of a yellow- 
ish tinge ; it is heavy, compact, and of a fine grain ; it is stronger and more 
durable than any other species, and on this account it is considered in- 
valuable for the purposes of ship-building, for which it is exclusively re- 
served. 

The live oak is not found further north than the neighborhood of Nor- 
folk, Virginia, nor further inland than from fifteen to twenty miles on the 
sea-coast. 

19o. Post Oak {Quercus obtusiloba). — This tree seldom attains a greater 
diameter than about fifteen inches, and on this account is mostly used for 
posts, from which use it takes its name. The wood has a yellowish hue 
and close grain ; is said to exceed white oak in strength and durability, 
and is therefore an excellent building material for the lighter kinds of 
frame-work. This tree is found most abundantly in the forests of Mary- 
land and Virginia, and is there frequently called Box White Oak and Iron 
Oak. It also grows in the forests of the Southern and Western States, but 
is rarely seen further north than the mouth of the Hudson River. 

196. Chestnut White Oak {Quercus prinus palustHs). — The timber of 
this tree is strong and durable, but inferior to the preceding species. The 
tree is abundant from North Carolina to Florida. 

197. Water Oak {Quercus aquatica). — This tree gives a tough but not 



62 



durable timber. It grows in the southern country from Virginia to as far 
south as Georgia and Florida. 

198. Red Oak (Quercus rubra). — This tree is found in all parts of the 
United States. The wood is reddish, of a coarse texture, and quite porous. 
The timber made from it decays quickly. 

199. Black Walnut (Juglans nigra). — The timber made from this tree is 
hard and fine-grained. It has become too valuable to be used in building 
purposes, except for ornamentation. 

200. Hickory {Juglans tomentosa). — The w r ood of this tree is tough and 
flexible. Its great heaviness and liability to be worm-eaten have prevented 
its general use in buildings. 

201. There are quite a number of other trees, belonging to both classes 
of hard and soft woods, that produce an inferior timber to those named, 
which have been occasionally used for building purposes. Tfrey may in 
the future be used to some extent. The Red Cedar, Chestnut, Ash, Elm, 
Poplar, American Lime or Basswood, Beech, Sycamore, Tamarack, etc., 
have all been used in constructions to a limited extent when the better va- 
rieties could not be obtained. 



CHAPTER VI. 
METALS. 



202. The metals used in engineering constructions are Iron, Steel, 
Copper, Zinc, Tin, Lead, and some of their alloys. 

208. Iron has the most extensive application of all the metals used for 
building purposes. It is obtained from the ore by smelting it in a blast- 
furnace. When coal is the fuel used, the air in a heated state high enough 
to melt lead is forced into the furnace, and this process is known as hot 
blast. 

\\ hen the metal lias fused, it is separated from the Other substances in 
the ore. and combines with a small percentage o[ carbon, from 2 to 5 per 
cent., forming a compound known as cast in>n. 

A sufficiency Of cast iron having accumulated in the furnace, it is 
lapped, and the molten metal runs out, being received in long, straight 
gutters formed in sand, which have numerous side branches. This 

arrangement Is called the sow and pigs; hence the name of pig-iron. 



63 



The iron is now in a shape to be sent to market, and in suitable eon- 
dition to be remelted and cast in the forms required, or converted into 
wrought or malleable iron. 

204. Impurities. — The strength and other good qualities of the iron 
depend mainly on the absence of impurities, and especially of those sub- 
stances known to cause brittleness and weakness, as sulphur, phosphorus, 
silicon, calcium, and magnesium. 

205. Cast Tron. — Cast iron is a valuable building material owing to its 
great strength, hardness, and durability, and the ease with which it can be 
cast or moulded into the best forms for the purposes to which it is to 
be applied. 

Cast iron is divided into two principal varieties, the gray east iron and 
white east iron. There exists a very marked difference between the pro- 
perties of these two varieties. These properties seem to depend upon the 
proportion of carbon and the state in which it is found in the metal. 
There are, besides, other intermediate varieties, which partake more or less 
of the properties of these two, as they approach, in their external appear- 
ances, nearer to the one or the other. 

206. Gray cast iron, when of good quality, is slightly malleable in a 
cold state, and will yield readily to the action of the file when the hard 
outside coating is removed. It has a brilliant fracture of a gray, some- 
times bluish gray, color. A medium-sized grain and close compact tex- 
ture indicate a good quality of iron. It is softer and tougher, and melts at 
a lower temperature, than white iron. 

207. White east iron is very brittle, resists the file and chisel, and is 
susceptible of high polish. Its fracture presents a silvery appearance, 
generally fine-grained and compact. 

Manufacturers distinguish the different varieties more particularly by 
numbers from 1 to 6, arranged according to their relative hardness, which 
apparently depends not so much on the total amount of carbon present in 
the specimen, as on the proportions respectively in a state of mechanical 
mixture and of chemical combination. 

APPEARANCES OF GOOD CAST IRON. 

208. The color and lustre presented by the surface of a recent fracture 
are the best indications of the quality of cast iron. A uniform dark-gray 
color and high metallic lustre are indications of the best and strongest. 
With the same color, but less lustre, the iron will be found to be softer and 



64 



weaker. That without lustre, of a dark and mottled color, is the softest 
and weakest of the gray varieties. 

Cast iron of a light-gray color and high metallic lustre is usually very 
hard and tenacious. As the color approaches to white, and the metallic- 
lustre changes to vitreous, hardness and brittleness become more marked 
until the extremes of a dull or grayish white color and a very high vitreous 
lustre are attained, which are the indications of the hardest and most 
brittle of the white variety. 

The quality of cast iron may also be tested by striking a smart stroke 
with a hammer on the edge of a casting. If the blow produces a slight 
indentation, without any appearance of fracture, it shows that the iron is 
slightly malleable, and therefore of a good quality ; if, on the contrary, 
the edge is broken, it indicates brittleness in the material, and a conse- 
quent want of strength. 

209. The strength of cast iron varies with its density; and this element de- 
pends upon the temperature of the metal when drawn from the furnace, 
the rate of cooling, the head of metal under which the casting is made, 
and the bulk of the casting. 

From all of these causes, by which the strength of iron may be in- 
fluenced, it is very difficult to judge of the quality of a casting by its exter- 
nal characters ; in general, however, if the exterior presents a uniform ap- 
pearance, devoid of marked inequalities of surface, it will be an indication 
of uniform strength ; and large castings are proportionally weaker than 
small ones. 

210. Wrought or Malleable Iron in its perfect condition is simply pure 
iron. It falls short of this to a greater or less extent, owing to the presence 
of impurities, some of which have been referred to in a previous para- 
graph. 

It may be made by direct reduction of the ore, but the common method is 
by the conversion of cast iron by the process called puddling. 

Itistough, malleable, and ductile. At a white heat it becomes soft enough 
to take any shape under the hammer, and admits of being melded. In order 
to weld two pieces together, each surface should he free from oxide. If 
there lie any present, it, is easily removed by sprinkling a little sand or dust 
over the surfaces to be joined, which forms a fusible* compound with the 
rust, which is readily squeezed out in the hammering or rolling. 

211. Quality. — The fracture Of good wroughl iron should have a clear 

"i;t\ color, metallic lustre, and a fibrous appearance. A crystalline struc- 



ture indicates, as a rule, defective wrought ir.on. Blisters, fair*, and cinder- 
holes are defects due to bad manufacture. 

212. Wrought Iron. — The strength of wrought iron is very variable, as 
it depends not only on the natural qualities of the metal, but also upon the 
care bestowed in forging, and the greater or less compression of its fibres 
when rolled or hammered into bars of different sizes. 

213. Forms. — The principal forms in which wrought iron is sent to mar- 
ket are Bur iron. Bound iron. Hoop and Sheet iron, and Wire. 

214. Bar iron comes in long pieces with a rectangular cross-section, gen- 
erally square, which is designated by 1 inch, 1\ inch, 2 inch, according 
to its dimensions. This is cut and worked into the shapes required. 

Bars receive various other forms of cross-section, depending upon the 
uses that are to be made of them. The best-knowm forms are the T, H or 
I, and L, from their general resemblance to these letters, and one of this 
shape, I \. The section like an inverted U is often seen. 

Rovnd iron comes in a similar form, except the cross-section is circular, 
and is known in the same way as 1 inch, 2 inch, etc. 

215. Hoop and Sheet iron are modifications of bar iron, the thickness 

being very small in comparison with the width. 

Cor rv anted iron is a modified form of 

Fig. 8. 
sheet 'iron, by winch its strength and A B 

stiffness are greatly increased. The dis- /^*~\*\ /^^T^\ 

tance between the corrugations, A B, Fig. •/ > ^ ^- L — _Ss- 

8, varies, being 3, 4, and 5 inches, and the 

depth of it, B C, being about one-fourth this distance. 

216. Iron Wire— The various sizes of wire might be considered as smaller 
sizes of round iron, being distinguished by numbers depending on the di- 
mensions of cross-section, except that wire is drawn through circular holes 
in a metal plate, to obtain the requisite cross-sections, not rolled, as round 
iron. These numbers run from to 36 ; No. wire having a diameter 
equal to one-third of an inch, and No. 36 one equal to .004 of an inch, the 
other numbers being contained between these and the whole series known 
as the Birmingham Wire Gauge. 

217. Steel and Steely Iron,— Steel, the hardest and strongest of the metals, 
is a chemical combination of iron and carbon which stands between wrought 
and cast iron. 

The term steely iron or semi-steel may be applied when the compound 
contains less than 0.5 per cent, of carbon ; more than this, and less than 2 



66 



per cent., the term steel ; and when 2 per cent, or more is present, the 
compound is cast iron, as before stated. 

218. Steel is made from iron by various processes, which may all be 
classed under tAvo heads, the one in which carbon is added to malleable 
iron, and the other, abstracting a part of the carbon from cast iron. Like 
iron, steel is seldom pure, containing other substances which, as a rule, 
affect it injuriously. There are, however, foreign substances which, 
introduced into the mass during manufacture, have a beneficial effect upon 
the steel by increasing its hardness and tenacity, and making it easier to 
forge and weld. 

219. The different kinds of steel arc known by names given them either 
from their mode of manufacture, their appearance, from some character- 
istic constituent, or from some inventor's process. 

Some of these arc natural steel, Mister steel, cast steel, shear steel, tilted 
steel, puddled steel, granulated steel, Bessemer steel, etc. 

220. Natural ox German steel is produced directly from the cast iron 
obtained from smelting the ore hj burning out a portion of the carbon 
which it contains. It is made principally in Germany, and is used in 
making files and other tools. 

221. Blister steel is made by a direct combination of malleable iron and 
carbon by a process known as "cementation." The bars, after being 
converted into steel, are found covered with blisters, from which it takes its 
name. It is brittle, and a fracture presents a crystalline appearance. 

222. Cast steel, known also as crucible steel, is made by breaking blis- 
tered steel into small pieces, and melting them in close crucibles, from which 
it is poured into iron moulds. The resulting ingot is then rolled or 
hammered into bars. 

This is the finest kind of steel, and best adapted for most purposes in the 
arts, but, from its expensiveness, not much used in building. 

Its fracture is of ji silvery color, homogeneous, with a tine, even, and 
close grain. It is very brittle, acquires extreme hardness, and is difficult to 
weld without a flux. 

228. Shear steel i^ made from blistered or natural steel by piling thin 
bars info fagots and working them until brought to a welding heat under 
heavy hammers or rolling into bars. [t is distinguished by the oames of 
half shear, ringU sfiear, and donbh shear, according to the number of times 
it has been piled. 

22 1 Tilted Bteel Is made from blistered steel moderatelv heated and sub- 



67 



jected to the action of a tilt or trip hammer, by which means its tenacity 
and density are increased. 

225. Puddled steel is made by puddling pig-iron, and stopping the pro- 
cess at the instant when the proper proportion of carbon remains. To all 
intents and purposes it is the same as natural steel. 

226. Granulated steel is made by allowing the melted pig-iron to fall 
into water, so that it forms into grains or small lumps, which are after- 
wards treated so as to acquire the proper proportion of carbon, and then 
melted together. 

227. Bessemer steel takes its name from the inventor of the process, and 
is made by direct conversion of cast iron into steel, which is run into large 
ingots. This conversion is effected either by decarbonizing the melted cast 
iron until only enough of carbon is left to make the required kind of steel, 
or, by removing all the carbon, adding to the malleable iron remaining in 
the furnace the necessary proportion of carbon. 

There are other kinds of steel, possessing certain characteristics peculiar 
to themselves or claimed for them, the process of making of which is not 
publicly known. 

228. Steel is more granular than iron, and much more easily melted, 
but the great difference between them is the power it has of becoming ex- 
tremely hard and elastic after being, tempered. The quality of steel de- 
pends in a great measure on the operation of hardening and tempering. 

It is hardened by heating it to a cherry -red color and suddenly cooling 
it by plunging it into some cold liquid. In this w T ay it is rendered so hard 
as to resist the hardest file, and very brittle. To give it the elastic property, 
it is tempered, which is done by heating the hardened steel to a certain de- 
gree, and cooling it quickly. The different degrees of heat will depend 
upon the use to which the steel is to be put. 

These qualities of hardness and elasticity adapt it for various uses for 
which neither cast nor wrought iron would be suitable. 

229. Durability of Iron and Steel. — Constructions in these metals are, like 
those in wood, liable to the same general conditions. They may be expos - 
ed to the air in a dry place, in a damp place, alternately wet and dry, or be 
entirely immersed in fresh or salt water. 

Their exposure to the air or moisture, especially if an acid be present, 
is followed by rusting, which proceeds with rapidity after it begins. The 
corrosion is more rapid when exposed to alternate wetness and dryness 
than in either of the other cases. 



230. Cast iron is usually coated with a film composed of a silicate of 
ferrous oxide, produced by the action of the sand of the mould on the melt- 
ed iron, which is very durable. If this be not injured, the casting will 
last a long time without rusting. 

231. Iron kept in a constant state of vibration rusts less rapidly than 
those which are at rest, 

232. Iron completely embedded in brick-work or masonry is preserved 
from rust, and in cathedrals and other ancient buildings has been found in 
good condition after six hundred years. It was protected by the lime in 
the mortar, which is a good preservative. 

233. The rapid deterioration of iron-work when exposed to the air and 
moisture makes the subject of increasing its durability by protecting it 
one of great importance. 

234. Protection of Iron- Work. — The ordinary means used to protect iron 
from rust are to cover its surface with some material that withstands the 
action of the air and moisture, even if it be for a limited time. 

The following are some of them : 

235. By painting . — The surface of the iron is covered with a coat of 
paint. Ked and white lead paints, ochreous or iron oxide paints, silicate 
paints, and bituminous paints are all used. The value of the paint for this 
purpose depends greatly upon the quality of the oil with which it is mixed. 
The painting must be renewed from time to time. 

^ 236. By japanning. — This name is given to the process in which the 
iron being placed in a heated chamber or furnace, and the paint applied, 
which to some extent is absorbed by the iron, a hard, smooth, varnish-like 
coating is formed over it, 

237. By the use of coal-tar. — In addition to applying coal-tar mixed 
with turpentine or other substances as a paint, it is used to protect iron by 
first heating the iron to about 000 c Fahr., and boiling it in the coal-tar. 

288. By the use of linseed-oil — The iron is heated, and the surface 
while hot is smeared over with cold linseed-oil. 

2;> ( .f. By galvanizing. — This term, "galvanized iron," is applied to arti- 
cles of iron coated with zinc. The iron, being thoroughly cleaned and 
Tree from scale, if dipped into a bath of melted zinc, will become perfectly 
coaled with il. This coating protects the iron from direct action of the 
air and moisi mv, and as long as it lasts intact the iron is pcrfeeth free 
from ni8l 

.'in. Oopper. — Tins metal possesses great durability under ordinarj 



exposure to the weather, and from its malleability and tenacity is easily 
manufactured into thin sheets and fine wire. 

When used for building purposes, its principal application is for roof- 
coverings, gutters and leaders, etc. Its great expense, compared with the 
other metals, forms the chief objection to its use. 

241. Zinc. — This metal, before it is made into sheets or other forms, is 
called spelter, and is used much more than copper in building, as it is much 
cheaper and exceedingly durable. Though subject to oxidation, the oxide 
does not scale off like that of iron, but forms an impervious coating, pro- 
tecting the metal under it from the action of the atmosphere, thus render- 
ing the use of paint unnecessary. 

It is very ductile, and can be easily bent into any required shape. 

The expansion and contraction caused by variations of temperature are 
greater for zinc than iron, and when it is used for roof-coverings particular 
attention must be paid that a plenty of play in the laps be allowed. 

242. Tin. — This metal is only used in building as a coating for sheet- 
iron or sheet-copper to protect their surfaces from oxidation. 

243. Lead. — This metal at one time was much used for roof-covering, 
lining of tanks, etc. It is now almost entirely superseded by the other 
metals. 

It possesses durability, but is wanting in tenacity, which requires thicker 
sheets to be used, in this way increasing the expense and the weight. 

244. Alloys. — An alloy is a compound of two or more metals, made by 
mixing them while in a melted state. Bronze, gun-metal, bell-metal, bras&j 
pewter, and the various solders are some of those that have a limited appli- 
cation to building purposes. 



CHAPTER VII. 
PAINTS, VARNISHES, ETC. 

245. Paints are mixtures of fixed and volatile oils, chiefly those of lin- 
seed and turpentine, with certain of the metallic salts and' oxides, and other 
substances which are used either as pigments or stainers, or to give what 
is termed a body to the paint, and also to improve its drying properties. 

246. Paints are mainly used as protective agents to secure wood and 
metals from the destructive action of air and w T ater. As they possess only 



70 



a limited degree of durability, they must be renewed from time to time. 
They are more durable in air than in water. 

247. The principal materials used in painting are : Red and white lead, 
red and yellow ochre, prussian blue, verdigris, lamp-black, litharge, linseed- 
oil, and spirits of turpentine. 

By combining these just named other colors may be obtained besides 
those directly given by them. A lead color is obtained by mixing a little 
lamp-black with the white lead, etc. 

Linseed-oil, being boiled with the addition of a .small quantity of lith- 
arge and sugar-of-lead forms what is known as drying oil. 

Spirits of turpentine is not generally used in the paints intended for 
external and finishing coats, as it does not stand exposure as well as oil. 

248. The first thing to be done before painting is to clean and smooth 
the surface to be painted. If the wood be resinous, the knots must be 
killed before the paint is applied, which is done by applying a coat of red 
lead mixed with sizing. The surface being dry, the first coat, generally 
white lead mixed with linseed-oil, is put on, which is called priming. This 
coat being dry, all holes, indentations, heads of nails, etc., should be filled 
and covered over with putty. The second coat of paint is then applied. 
If it be old work that is to be repainted, the entire surface should be 
scrubbed with soap and water, well scraped, and then rubbed down with 
sand-paper or pumice to get rid of the old paint and obtain an even, smooth 
surface. 

249. Varnishes. — They are made by dissolving resinous substances in 
alcohol or linseed-oil and spirits of turpentine, just as paints are made by 
dissolving or mixing pigments. 

They are used for the same purposes as paints, and to give a clear, shin- 
ing appearance to the surface on which they are laid. 

250. (Hazing is the art of fixing glass in the frames of windows. The 
panes are secured with putty, which is a composition of whiting and lin- 
seed-oil, with sometimes an addition of white lead. Large panes should 
be additionally secured by means of small nails or brads. 



/ 



AN 

\ 

ELEMENTARY COURSE 



Civil Engineering 



FOB THE USE OP 



CADETS OF THE UNITED STATES MILITARY ACADEMY. 



JY BrWHEELER, 



Professor of Civil and Military Engineering in the United States Military Academy at 
West Point, JV. •'¥-., and Brevet-Colonel U. S. Army. 



New York: 

printed foe the it. s. military academy, 



BY 

JOHN WILEY & SONS. 
1876. 



Copyrighted, 1876, by 
JOHN WILEY & SONS. 



John F. Trow & Son, 
Printers and Bookbinders, 

i ; Bast \:tk St., 
.1 M YORK. 






CA PREFACE 



W 



The following treatise has been compiled and arranged especially 
for the use of the cadets of the United States Military Academy, 
and with regard to the limited time allowed them for instruction 
in this branch of their studies. 

An attempt has been made in the following pages to give in a 
concise form the general principles of Civil Engineering and their 
applications, as presented in the writings and practice of civil 
engineers of standing in the profession. 

To the beginner, all will be new ; but to the well-informed 
engineer, the sources from which the contents of this treatise have 
been derived will be readily recognized. 

The general arrangement adopted in the work varies slightly 
from the one used by my predecessor, the late Prof. Mahan, but his 
impress is seen throughout, even in many cases in the use of his 
exact words. 

The chapter on Limes and Cements is based almost entirely on 
the printed works of General Gillmore, of the U. S. Engineers, 
and on a manuscript article which he kindly furnished me for the 
purpose. 

To Lieut. W. H. Bixby, Corps of Engineers, U. S. A., I am 
indebted for many valuable suggestions and much assistance in 
preparing this work. 

J. B. W. 

"United States Military Academy, West Point, N. Y., May 30, 1876. 



INTRODUCTORY CHAPTER. 



I. Engineering is defined to be " the science and art of 
utilizing the forces and materials of nature." 

It is divided into two principal branches, Civil and Military 
Engineering. 

The latter embraces the planning and construction of all de- 
fensive and offensive works used in military operations. 

The former comprises the designing and building of all works 
intended for the comfort of rnau, or to improve the country either 
by beautifying it or increasing its prosperity. 

In this branch the constructions are divided into two classes, 
according as the parts of which they are made are to be relatively 
at rest or in motion. In the former case they are known as 
structures, and in the latter as machines. 



II. It is usual to limit the term civil engineering to the 

planning and construction of works of the first class, and to use 
the term mechanical or dynamical engineering when the 
works considered are machines. 

It is also usual to subdivide civil engineering into classes, 
according to the prominence given to some one or more of its parts 
when applied in practice, as topographical engineering ', hydraulic 
engineering ', railway engineering, etc. By these divisions, greater 
progress toward perfection is assured. Notwithstanding this sepa- 
ration into branches and subdivisions, there are certain principles 
which are general. 



& x 



III. The object of the following pages is to give in regular order 
those elementary principles, common to all branches of engineer- 
ing, which it is essential for the student to learn, that he may 
understand the nature of the engineer's profession, and know how 
to apply the principles that he has already acquired. 



VI INTRODUCTORY CHAPTER. 

IV. A structure is a combination of portions of solid materials 
so arranged as to withstand the action of any external forces to 
which it may be exposed, and still to preserve its form. These 
portions are called pieces, and the surfaces where they touch and 
are connected are called joints. The term solid here used is 
applied to a body that offers an appreciable resistance to the action 
of the different forces to which it may be subjected. 

V. That part of the solid material of the earth upon which the 
structure rests is called the foundation, or bed of the founda- 
tion, of the structure. 

VI. In planning and building a structure, the engineer should 
be governed by the following conditions : 

The structure should possess the necessary strength ; should 
last the required time ; and its cost must be reasonable. 
In other words, the engineer in projecting and executing a w T ork 
should duly consider the elements of strength, durability, and 
economy. 

VII. The permanence of a structure requires that it should 
possess stability, strength, and stiffness. It will possess these 
when the following conditions are fulfilled : 

When all the external forces, acting on the whole structure, are 
in equilibrium ; 

When those, acting on each piece, are in equilibrium ; 

When the forces, acting on each of the parts into which a piece 
may be conceived to be divided, are in equilibrium ; and 

When the alteration in form of any piece, caused by the exter 
nal forces, does not pass certain prescribed limits. 

A knowledge, therefore, of the forces acting on the structure 
and of the properties of the materials to be used in its construc- 
tion, is essential. 

VIII. The designing and building of a structure form three dis 
tine 1 operations, as follows : 

1. The conception of the project or plan; 

2. Putting (his on paper, so it can be understood; and 
8. I is execution. 



LNTRODUCTOKY CHAPTER. Vll 

The first requires a perfect acquaintance with the locality where 
the structure is to be placed, the ends or objects to be attained by 
it, and the kind and quantity of materials that can be supplied at 
that point for its construction. 

The second requires that the projector should know something 
of drawing, as it is only by drawings and models accompanied by 
descriptive memoirs, with estimates of cost, that the arrangement 
and disposition of the various parts, and the expense of a proposed 
work, can be understood by others. 

The drawings are respectively called the plan, elevation, and 
cross-section, according to the parts they represent. A sym- 
metrical structure requires but few drawings ; one not symmetri- 
cal, or having different fronts, will require a greater number. 

These, to be understood, must be accompanied by written speci- 
fications explaining fully all the parts. 

The estimate of cost is based upon the cost of the materials, the 
price of labor, and the time required to finish the work. 

The third may be divided into three parts : 

1. The field-work, or laying out the work ; 

2. The putting together the materials into parts ; and 

3. The combining of these parts in the structure. 

This requires a knowledge of surveying, levelling, and other 
operations incident to laying out the work ; 

A knowledge of the physical properties of the materials used ; 

The art of forming them into the shapes required ; and 

How they should be joined together to best satisfy the condi- 
tions that are to be imposed upon the structure. 




/- - ■> 



fen 



ELEJVXEJSTTARY COURSE 



OF 



CIVIL ENGINEERING. 



PART I. 

BUILDING MATERIALS. 

1. The materials in general use for civil constructions may 
be arranged in three classes : 

1st. Those which constitute the more solid components of 
structures; as Wood, Stone, and the Metals. 

2d. Those which unite the solid parts together; as Glue, 
Cements, Mortars, Mastics, etc. 

3d. The various mixtures and chemical preparations em- 
ployed to coat the solid parts and protect them from the 
action of the weather and other causes of destructibility ; as 
Paints, Solutions of Salts, Bituminous Substances, etc. 



CHAPTEE I 
WOOD. 



2. The abundance and cheapness of this material in the 
United States, the ease with which it could be procured and 
worked, and its strength, lightness, and durability, under 
favorable circumstances, have caused its very general use in 
every class of constructions. 

Timber, from the Saxon word timbrian, to build, is the 
term applied to wood of a suitable size, and fit for building 
purposes. While in the tree it is called standing timber ; 
after the tree is felled, the portions fit for building are cut 
into proper lengths and called logs or rough timber ; when 
the latter have been squared or cut into shape, either to be 



2 CIVIL ENGINEERING. 

used in this form or cut into smaller pieces, the general term 
timber is applied to them ; if from the trunk of the tree, 
they are known as square or round, hewn or sawed, accord- 
ing to the form of cross-section and mode of cutting it ; if 
from the branches or roots, and of crooked shape, they are 
called compass timber. The latter is used in ship-building. 

The logs, being sawed into smaller pieces, form lumber, 
and the latter is divided into classes known as joists, scant- 
lings, strips, boards, planks, etc., and, when sawed to suit a 
given bill ; as dimension stuff. 

3. The trees used for timber are exogenous — that is, they 
grow or increase in size by formation of new wood in layers 
on its onter surface. 

If the trunk of a tree is cut across the fibres, the cut will 
show a series of consecutive rings or layers. 

These layers are of annual growth in the temperate zones, 
and, by counting them, the approximate age of the tree may 
be determined. 

The trunk of a full-grown tree presents three distinct 
parts : the bark, which forms the exterior coating ; the sap- 
wood, which is next to the bark ; the heart, or inner part, 
which is easily distinguishable from the sap-wood by its 
greater density, hardness and strength, and oftentimes by its 
darker color. 

The heart embraces essentially all that part of the trunk 
which is of use as a building material. The sap-wood 
possesses but little strength, and is subject to rapid decay, 
owing to the great quantity of fermentable matter contained 
in it; and the bark is not only without strength, but, if 
suffered to remain on the tree after it is felled, it hastens the 
decay of the sap-wood and heart. 



VARIETIES OF TIMBER-TREES LN THE UNITED STATES. 

4. The forests of our own country produce a great variety 
of the best timber for every purpose. For use in construc- 
tion, timber is divided into two general classes, soft wood 
and hard wood. 

The first Includes all coniferous trees, like the pines, and 

also some few varieties of the leai'-wood trees; and the 

other includes most of the timber trees that are non-conifer- 
ous, like the oaks, etc. 

The Boft wood trees generally contain turpentine, and are 
distinguished by straightness oi fibre and by the regularity 
oi form oi the tree. The timber made From them is moro 



TIMBER. 



easily sawed or split along the grain, and much more easily 
broken across the grain, than that of the second class. 

The hard-wood, or non-coniferous timber, contains no tur- 
pentine, and, as a class, is tough and strong. 



EXAMPLES OF SOFT-WOOD TREES. 

5. Yellow Pine {Pinus variabilis). — The heart-wood of 
this tree is fine-grained, moderately resinous, strong and 
durable ; but the sap-wood is very inferior, decaying rapidly 
on exposure to the weather. The timber is in very general 
use for frame-work, etc. 

This tree is found throughout our country, but in the 
greatest abundance in the Middle States. In the Southern 
States it is known as Spruce Pine and Short-leaved Pine. 

Long-leaved Pine, or Southern Pine {Pinus palustr is). 
— This tree has but little sap-wood ; the resinous matter is 
uniformly distributed throughout the heart-wood, which pre- 
sents a fine compact grain, and which has more hardness, 
strength, and durability than any other species of the pine ; 
on account of these qualities, its timber is in very great 
demand for certain constructions. 

The tree grows as far north as Virginia, and from this 
district southward it is abundantly found. 

White Pine, or Northern Pine {Pinus strobus). — This 
tree takes its name from the color of its wood, which is 
white, soft, light, straight-grained, and durable. The timber 
from it is inferior in strength to the species just described, 
and has, moreover, the defect of swelling in damp weather. 
It is, however, in great demand as a building material, being 
extensively used throughout the Eastern and Northern 
States. The tree is found between the 43d and 47th par- 
allels of north latitude, the finest specimens growing in 
Maine. 

Norway Pine {Pinus rubra). — This is a species found in 
the north-west, especially in Michigan and Wisconsin, where 
it ranks very high, comparing favorably with the common 
yellow pine, although having less resin in it. 

6. Fir. — The genus Fir {Abies), commonly known as 
Spruce, furnishes large quantities of timber and lumber, 
which are extensively used throughout the Northern States. 
-The lumber made from it has the defects of twisting and 
splitting on exposure to the w T eather and decaying rapidly in 
damp situations. The common fir {Abies alba and Abies 
nigra), the spruce fir found in Northern California, and the 



4 CIVIL ENGINEERING. 

Oregon fir [Pinus {Abies) Douglasii] which grows to an 
enormous size, all furnish timber much used in building. 

7. Hemlock (Abies Canadensis) is a well-known species, 
used throughout the Northern States as a substitute for pine 
when the latter is difficult or expensive to procure. It ifc 
very perishable in moist situations or when subjected to alter- 
nate wetness and dryness. It has been used in considerable 
quantities in the Government works on the Lakes in positions 
where it is entirely submerged in fresh water. Hemlock tim- 
ber is often shaky, full of knots, and splits more easily when 
framing it than pine. 

8. Cedar. — The Juniper or White Cedar, and the Cypress 
are very celebrated for affording a material which is very 
light and which is of great durability when exposed to the 
weather; on this account, it is almost exclusively used for 
shingles and other exterior coverings. These two trees are 
found in great abundance in the swamps of the Southern 
States. 

9. The foregoing kinds of timber, especially the pines, are 
regarded as valuable building materials, on account of their 
strength, their durability, the straightness of the fibre, the 
ease with which they are worked, and their applicability to 
almost all the purposes of constructions in wood. 



EXAMPLES OF HAED-WOOD TEEES. 

10. White Oak (Quercvs alba). — The bark of this tree is 
light, near!} 7 white; the leaf is long, narrow, and deeply in- 
dented ; the wood is compact, tough, and pliable, and of a 
straw color with a pinkish tinge. 

It is largely used in ship-building, the trunk furnishing the 
necessary timber for the heavy frame-work, and the roots and 
large branches affording an excellent quality of compass-tim- 
ber. Boards made from it are liable to warp and crack. 
This tree grows throughout the United States and Canada, but 
most abundantly in the Middle States. Proximity to salt air 
during the growth of the tree appears to improve the quality 
of the timber. The character of the soil has a decided effect 
on it. In a moist soil, the tree grows to a larger size, but 
the timber loses in firmness and durability. 

Live Oak (Quercu8 virens). — The wood of this tree is of 
a yellowish tinge; it is heavy, compact, and ot" a fine grain; 
it is si ranger and more durable than that of any other species, 

and '>n this accounl is considered invaluable for the purposes 

of ship-bttflding, tot which it has been exclusively reserved, 



TIMBER. 

The live oak is not found further north than the neighbor- 
hood of Norfolk, Virginia, nor further inland than from fif- 
teen to twenty miles from the sea-coast. 

Post Oak (Que reus ohtusiloba). — This tree seldom attains 
a greater diameter than about fifteen inches, and on this 
account is mostly used for posts, from which use it takes its 
name. The wood has a yellowish hue and close grain ; is said 
to exceed white oak in strength and durability, and is there- 
fore an excellent building material for the lighter kinds of 
frame-work. This tree is found most abundantly in the 
forests of Maryland and Virginia, and is there frequently 
called Box White Oak and Iron Oak. It also grows in the 
forests of the Southern and Western States, but is rarely seen 
further north than the southern part of New York. 

Chestnut White Oak (Quereus prinus palustris). — The 
timber of this tree is strong and durable, but inferior to the 
preceding species. Theiree is abundant from North Carolina 
to Florida. 

Water Oak (Quereus aqicatica). — This tree gives a tough 
but not durable timber. It grows in the Southern country 
from Virginia to as far south as Georgia and Florida. 

Red Oak (Quereus rubra). — This tree is found in all parts 
of the United States. The wood is reddish, of a coarse tex- 
ture, and quite porous. The timber made from it decays 
quickly. 

11. Black Walnut (Juglans nigra). — The timber made *' u 
from this tree is hard and fine-grained. It has become too 
valuable to be used in building purposes, except for orna- 
mentation. 

Hickory (Juglans tomentosa). — The wood of this tree is 
tough and flexible. Its great heaviness and liability to be 
worm-eaten have prevented its general use in buildings. 

12. There are quite a number of other trees, belonging to 
both hard and soft woods, that produce an inferior timber to 
those named, and have been occasionally used for building 
purposes. They may possibly in the future be used to some 
extent. The Red Cedar, Chestnut, Ash, Elm, Poplar, Ameri- 
can Lime or Basswood, Beech, Sycamore, Tamarack, etc., 
have been used to a limited extent in constructions when the 
better varieties could not be obtained. 



PREPARATION OF TIMBER. 

13. Felling". — Trees should not be felled for timber until 
they have attained their mature growth, nor after they ex- 



/ffW *J 



CIVIL ENGINEERING. 



hibit symptoms of decline ; otherwise the timber will not pos- 
sess its maximum strength and durability. Most forest trees 
arrive at maturity in between fifty and one hundred years, 
and commence to decline after one hundred and fifty or two 
hundred years. When a tree commences to decline, the 
extremities of its older branches, and particularly its top, 
exhibit signs of decay. The age of a tree can, in most cases, 
be approximately ascertained either by its external appear- 
ances or by cutting into the centre of its trunk and counting 
the rings or layers of the sap and heart. 

. Trees should not be felled while the sap is in circulation ; 
for this substance is of such peculiarly fermentable nature, 
that if allowed to remain in the fallen timber, it is very pro- 
ductive of destruction of the wood. The best authorities on 
the subject agree that the tree should be felled in the win- 
ter season. 

The practice in the United States accords with the above, 
not so much on account of the sap not being in circulation, 
as for the reason that the winter season is the best time for 
procuring the necessary labor, and the most favorable for re- 
moving the logs, from where they are cut, to the points where 
they are to b© made into rafts. 

As soon as the tree is felled, it should be stripped of its 
bark and raised from the ground. A short time only should 
elapse before the sap-wood is taken off and the timber reduced 
nearly to its required dimensions. 

14:. Measuring Timber. — Timber is measured by the 
cubic foot, or by hoard meastire, the unit of which is a super- 
ficial foot of a board one inch thick. 



APPEARANCES OF GOOD TIMBER. 

15. Among trees of the same species, that one which has 
grown the slowest, as shown by the narrowness of its annual 
rings, will in general be the strongest and most durable. 

The grain should be hard and compact, and if a cut be 
made across it, the fresh surf ace of the cut should be firm and 
shining. 

And, in general, other conditions being the same, the 
strength and durability of timber will increase with its weight, 
and darkness of color. 

Timber of good quality should be straight-grained, and 
five from knots. It should be five from all blemishes and 
delects. 



TIMBER. 



DEFECTS IN TIMBER. 



16. Defects arise from some peculiarity in the growth of 
the tree, or from the effects of the weather. 

Strong winds oftentimes injure the growing tree by twist- 
ing or bending it so as to partially separate one annual layer 
from another, forming what is known as rolled timber or 
shakes. 

Severe frosts sometimes cause cracks radiating from the 
centre to the surface. ' 

These defects, as well as those arising from worms or age, 
may be detected by examining- a cross-section of the log. 



SEASONING- OF TIMBER. 

17. Timber is said to be seasoned when by some process, 
either natural or artificial, the moisture in it has been ex- 
pelled so far as to prevent decay from internal causes. 

By the term, seasoning, is meant not only the drying which 
expels, but also a removal or change of the albuminous sub- 
stances. The latter are fermentable, and, when present un- 
changed in the timber, are ever ready to promote decay. 

The seasoning of timber is of the greatest importance, not 
only to its own durability, but to the solidity of the structure 
for which it may be used ; for, if the latter, when erected, 
contained some pieces of unseasoned or green timber, their 
after-shrinking might, in many cases, cause material injury, 
if not complete destruction, to the structure. 

Natural Seasoning consists in exposing the timber freely 
to the air, but in a dry place, sheltered from the sun and high 
winds. 

This method is preferable to any other, as timber seasoned 
in this way is both stronger and more durable than when pre- 
pared by any artificial process. It will require, on an aver- 
age, about two years to season timber thoroughly by this 
method. For this reason, artificial methods are used, to save 
time. 

Water Seasoning, — The simplest artificial method consists 
in immersing the timber in water as soon as cut, care being 
taken to keep it entirely submerged, and then, after a fort- 
night's soaking, in removing it to a suitable place and drying 
it. The water will remove the greater portion of the sap, 
even if the timber is full when immersed. This method 
doubtless weakens the timber to some extent, and therefore 



8 CIVIL ENGINEERING. 

is not recommended where strength is of material importance 
to the timber. 

Boiling and Steaming have both been used for seasoning, 
but are open to the same objection as the last method ; viz., 
the impairing of the elasticity and strength of the timber. 

Hot-air Process. — This consists in exposing the timber in 
a chamber, or oven, to a current of hot air, whose temperature 
varies according to the kind and size of the timber to be sea- 
soned. This is considered the best of the artificial methods. 
The time required for sufficient seasoning depends upon the 
thickness of the timber, ordinary lumber requiring from one 
to ten weeks. 



DURABILITY AND DECAY OF TTMBER. 

18. Timber lasts best when kept, or used, in a dry and 
well-ventilated place. Its durability depends upon its pro- 
tection from decay and from the attacks of worms and insects. 

The wet and dry rot are the most serious causes of the 
decay of timber. 

Wet Rot is a slow combustion, a decomposition of moist 
organic matter exposed to the air without sensible elevation 
of temperature. The decay from wet rot is communicated 
only by contact, and requires the presence of moisture. 

To guard against this kind of rot, the timber must not be 
subjected to a condition of alternate wetness and dryness, or 
even a slight degree of moisture, if accompanied by heat and 
confined air. 

Dry Rot is a disease of timber arising from the decompo- 
sition of the albumen and other fermentable substances 
accompanied by the growth of a fungus, whose germs spread 
in all directions without actual contact being necessary, and 
it finally converts the wood into a fine powder. The fungus 
is not the cause of decay; it only converts corrupt matter 
into new forms of life. 

Dry rot derives its name from the effect produced and not 
from the cause, and although it is usually generated in mois- 
ture, in some cases it flourishes independent of extraneous 
humidity. Externally, it makes its first appearance as a mil- 
dew, or a white or yellowish vegetation like it in appearance. 
Aii examination under a, microscope of a section of a pieceof 
wood, attacked by dry rot, shows minute white threads spread* 
in! ramifying throughout its substance. Dry mi attacks 
only wood which is dend, whereas wet rot may seize the tree 
while it is still alive and standing. Timber not property sea- 



TIMBER. 

sonecl, used where there is a want of free circulation of air, de- 
cays by this disease even if there be only a small amount of 
moisture present. It will also decay by dry rot, if covered 
while unseasoned by a coat of paint, or similar substance. 



DURABILITY UNDER CERTAIN CONDITIONS, AND MEANS OF 
1 INCREASING IT. 

19. Timber may be subjected to the following conditions : 

It may be kept constantly dry, or at least practically so. 

It may be kept constantly wet in fresh water. 

It may be constantly damp. 

It may be alternately wet and dry. 

It may be constantly wet in sea-water. 

20. Timber kept constantly dry in well-ventilated posi- 
tions, will last for centuries. The roof of Westminster Hail 
is more than 450 years old. In Stirling Castle are carvings 
in oak, w T ell preserved, over 300 years old ; and the trusses of 
the roof of the Basilica of St. Paul, Home, were sound and 
good after 1000 years of service. The timber dome of St. 
Mark, at Venice, was in good condition 850 years after it was 
built. 

It would seem hardly worth while to attempt to increase 
the durability of timber when under these conditions, except 
where it may be necessary to guard against the attacks of in- 
sects, which are very destructive in some localities. Slaked 
lime hastens the decay of timber ; the latter should therefore, 
in buildings, be protected against contact with the mortar. 

21. Timber kept constantly wet in fresh "water, under 
such conditions as will exclude the air, is also very durable. 

Oak, elm, beach, and chestnut piles and planks were found 
beneath the foundation of Savoy Place, London, in a perfect 
state of preservation, after having been there 650 years. 
. The piles of the old London Bridge were sound 800 years 
after they were driven. In the bridge built by Trajan, the 
piles, after being driven more than 1600 years, were found to 
have a hard exterior similar to a petrifaction, for about four 
inches, the rest of the wood being in its ordinary condition. 

We may conclude that timber submerged in fresh water 
will need no artificial aid to increase its durability, although in 
time it may 'be somewhat softened and weakened. 

22. Timber in damp situations. — Timber in damp sit- 
uations is in a place very unfavorable for its durability, and is 
liable, as previously stated, to decay rapidly. In such situa- 



10 CIVIL ENGINEERING. 

tions only the most lasting material is to be employed, and 
every precaution should be taken to increase its durability. 

There are at our command three means for increasing the 
durability of timber in damp situations : 

1st. To season it thoroughly. 

2d. To keep a constant circulation of air about it. 

3d. To cover it with paint, varnish, or pitph. 

The first of these means is essential to the others, and may 
be combined with either or both of them. 

The cellulose matter of the woody fibre is very durable when 
not acted upon by fermentation, and the object of seasoning is 
to remove or change the fermentable substances, as well as to 
expel the moisture in the timber, thus protecting the cellulose 
portion from decay. Even if the timber be well seasoned, 
thorough ventilation is indispensable in damp situations. 

The rapid decomposition of sills, sleepers, and lower floors 
is not surprising where neither wall-gratings nor ventilating 
flues carry off the moisture rising from the earth or the foul 
gases evolved in the decay of the surface-mould. The lower 
floors will last nearly as long as the upper ones if we remove 
the earth to the bottom of the foundation, and fill in the cavity 
with diy sand, plaster rubbish, etc., or lay down a thick 
stratum of cement or concrete to exclude the water, and pro- 
vide for a complete circulation of air. While an external 
application of paint, or pitch, or oil laid on hot increases the 
durability of well-seasoned timber, nothing can more rapidly 
hasten decay than such a coating upon the surface of green 
timber. This mistake is daily made. The coating of paint 
closes the pores of the outer surface, and prevents the es- 
cape of the moisture from within, thus retaining in the wood 
the elements of decay. 

23. Timber alternately wet and dry. — The surface of 
all timber exposed to alternations of wetness and dryness grad- 
ually wastes away, becoming dark-colored or black. This is 
wet rot, or simply " rot. " 

I )ensity and resinonsness exclude moisture to a great extent ; 
hence timber possessing these qualities should be used in such 
situations. Heart-wood, from its superior density, is more du- 
pable than Bap-wood ; oak, than poplar or willow. Resinous 
wood, :is pine, is more durable than the non-resinous, as ash or 
beech, in such situations. 

24. Timber constantly wet in sea- water.— Tl ie re- 
marks made about timber placed in fresh water apply equal- 
ly bo thie case, as far as relates to decay from rot. Timber 
immersed in Ball water is however liable to the attacks of two 



TIMBER. 11 

of tlie destructive inhabitants of our waters, the Limnoria 
terebrans and Teredo navalis ; the former rapidly destroys 
the heaviest logs by gradually eating in between the annual 
rings ; and the latter, the well-known ship-worm, converts 
timber into a perfectly honeycombed state by its numerous 
perforations. They both attack timber from the level of the 
mud, or bottom of the water, and work to a height slightly 
above mean low- water. The timber, for this distance, must be 
protected by sheathing it with copper, or by thickly studding 
the surface with broad-headed iron nails, or other similar de- 
vice. Resinous woods resist their attacks longer, most prob- 
ably on account of the resin in the wood. The resin is after 
a time washed or dissolved out, and the timber is speedily 
attacked. 

An examination of piles in the wharf at Fort Point, San 
Francisco harbor, where these agents are very destructive, 
showed that piles which were driven without removing the 
bark, resisted, to a certain extent, their destructive attacks. 

Timber saturated with dead oil, by the process known as 
creosoting, has been stated to offer an effective resistance. 

PRESERVATION OF TIMBER. 

25. The necessity of putting timber in damp places, or 
where it will be exposed to alternate wetness and dryness, has 
caused numerous experiments to be made with reference to 
increasing its durability under such circumstances by pre- 
venting or delaying its decay. 

There are many patented processes, having this object in 
view, based either on the principle of expelling the albumin- 
ous substances and replacing them by others of a durable na- 
ture, or on that of changing the albuminous substances into 
insoluble compounds by saturating the timber with salts of an 
earthy or metallic base which will combine with the albumin- 
ous substance. 

Some of the processes which have been proposed, or used, 
are as follows : 

Kyanizing. — Kyan's process is to saturate the timber with 
a solution of chloride of mercury, one pound of the chloride 
to four gallons of water. 

The complete injection of the liquid is obtained either by 
long immersion in the liquid in open vats, or by great pressure 
upon both solution and wood in large wronght-iron tanks. 

The expensiveness of the process, and its unheal thiness to 
those employed in it, forbid its extensive use. 









12 CIVIL ENGINEEEING. 

Burnettizing. — Burnett's process is to use a solution of 
chloride of zinc, one pound of the chloride to ten gallons of 
water; the solution being forced into the wood under a pres- 
sure of 150 pounds to the square inch. 

Earle's Process consisted in boiling the timber in a solu- 
tion of one part of sulphate of copper to three parts of the 
sulphate of iron ; one gallon of water being used with every 
pound of the salts. A hole was bored through the whole 
length of the piece ; the timber was then immersed from two 
to four hours, and allowed to cool in the mixture. 

Ringold and Earle invented the following process : A hole 
from J to 2 inches in diameter was made the whole length of 
the piece, and the timber boiled from two to four hours in 
lime-water. After the piece was dried, the hole was filled with 
lime and coal-tar. Neither of the last two methods was very 
successful. . 

Common Salt is known in many cases to be a good 
preservative. According to Mr. Bates's opinion this method 
often answers a good purpose if the pieces so treated are 
not too large. 

Boueherie's Process employs a solution of sulphate of cop- 
per or pyrolignite of iron. One end of the green stick is en- 
closed in a close-fitting collar, to which is attached a water- 
tight bag communicating through a flexible tube with an 
elevated reservoir containing the solution. Hydrostatic pres- 
sure soon expels the sap. When the solution issues in a pure 
state from the opposite end of the log, the process is complete. 

It was found that the fluid will pass a distance of twelve 
feet along the grain under less pressure than is necessary to 
force it across the grain three-fourths of an inch. The opera- 
tion is performed upon green timber with great facility. 

In 1846, 80,000 railroad ties of the most perishable woods, 
impregnated, by Boueherie's process, with sulphate of copper, 
were laid down on French railways. After nine years' expo- 
sure they were found as perfect as when laid. This experi- 
ment was so satisfactory that most of the railways of that 
country at once adopted the process. It has been suggested 
to wash out the sap with water, which would not coagulate 
the albumen, and then to use the solution. 

Bethel's Process. — The timber is placed in an airtight 
cylinderof boiler-iron, and the air partially exhausted. Dead 
oil is thou admitted at a temperature or 120° Fahr., and a. 
pressure of about L50 pounds to the square inch is then ap- 
plied, and maintained Brom five to eight hours, according to 
ize <>f the timbers under treatment. The oil is then 

drawn oft, and the timber is removed. 



STONE. 13 

The Seeley Process consists in subjecting the wood, while 
immersed in dead oil, to a temperature between 212° and 
300° Fahr. for a sufficient length of time to expel any mois- 
ture present ; the water being expelled, the hot oil is quickly 
replaced by cold, thus condensing the steam in the pores of 
the timber, forming a vacuum into which oil is forced by at- 
mospheric pressure and capillary attraction. In this process 
from six to twelve pounds of oil for each cubic foot of wood 
is expended. 

The theory of this process is that the first part of the opera- 
tion seasons the wood, destroys or coagulates the albumen, 
and expels the moisture ; and that the second part fills the 
wood-cells with a material that is an antiseptic and resists de- 
structive agents of every kind. 

Robbins's Process consists in treating timber with coal-tar 
in the form of vapor. 

The wood is placed in an air-tight iron chamber, with 
which is connected a still or retort, over a furnace. The fur- 
nace is then fired and the wood kept exposed to the vapors 
produced by the heat from six to twelve hours; the opera- 
tion is then considered complete. 

The most improved of all these methods is Seeley's; this 
is a modification and an improvement of Bethel's process, and 
is generally known as " ereosoting." 

It is thought that the ancient Egyptians knew of some pro- 
cess of preserving wood. Old cases, supposed to have been 
2,000 years old, apparently of sycamore impregnated with 
bitumen, have been found to be still perfectly sound and 
strong. 



CHAPTEK II. 

STONE. 



26. The qualities required in stone for building purposes 
are so various that no very precise directions can be given to 
exactly meet any particular case. What would be required 
for a sea-wall would not answer for a dwelling-house. In 
most cases the choice is limited by the cost. The most 
essential properties of stone as a building material are 
strength, hardness, durability, and ease of working. 
These properties are determined by experience or actual 
experiment. 



14 CIVIL ENGINEERING. 

27. The term Stone, or Rock, is applied to any aggregation 
of several mineral substances, and, as a building material, 
may be either natural or artificial. 

Natural Stones may be subdivided into three classes ; the 
silieious, the argillaceous, and the calcareous, according as 
silica, alumina, or lime is the principal constituent. 

Artificial Stones are imitations of natural stone, made by 
consolidating fragmentary solid material by various means; 
they may be subdivided into classes as follows : 

1st. Those in which two or more kinds of solid materials 
are mixed together and consolidated by baking or burning ; 
as brick, tiles, etc. 

2d. Those in which the solid materials are mixed with 
some fluid or semi-fluid substance, which latter, hardening 
afterwards by chemical combinations, binds the former firmly 
together ; as ordinary concrete, patent stone, etc. 

3d. Those in which the solid materials are mixed with 
some hot fluid substance which hardens upon cooling; as 
asphaltic concrete, etc. 



I. NATUEAL STONES. 

GENERAL OBSERVATIONS ON THE PROPERTIES OF STONE AS A 
BUILDING MATERIAL. 

28. Strength, hardness, durability, and ease of working 

have already been mentioned as essential properties to be 
considered in selecting stone for building purposes. 

It is not easy to judge of the qualities from external 
appearances. In most cases stone, which has one of the 
three properties first named, will have also the other two. In 
general, when the texture is uniform and compact, the grain 
fine, the color dark, and the specific gravity great, the stone 
is of good quality. If there are cracks, cavities, presence 
of iron, etc., even though it belong to a good class of stone, it 
will be deficient in some of these essential qualities, and 
should be rejected. A coarse stone is ordinarily brittle, and 
is difficult to work ; it is also more liable to disintegrate than 
that of a finer grain. 

29. Strength. — Among stones of the same kind, the strong- 
est is almost always that which has the greatest heaviness. 

As stone is ordinarily to be subjected only to a crushing force, 
it will only lx* in particular cases that the resistance to this 
strain need be considered, the strength of stone in this respect 
being greater than is generally required of it. 11' its dura- 



STONE. 15 

bilitj is satisfactorily proved, its strength, as a rule, may be 
assumed to be sufficient. 

30. Hardness. — This property is easily ascertained by 
actual experiment and by a comparison made with other 
stones which have been tested. It is an essential quality in 
stone exposed to wear by attrition. Stone selected for paving, 
nagging, and for stairs should be hard and of a grain too 
coarse to admit of becoming very smooth under the action to 
which they are submitted. 

By the absorption of water, stones become softer and more 
friable. 

31. Durability. — By this term is meant the power to resist 
the wear and tear of atmospheric causes when exposed to their 
influence, the capacity to sustain high temperature, and the 
ability to resist the destructive action of fresh and salt water. 

The appearances which indicate probable durability are 
often deceptive. 

As a general rule, those stones of the same hind which are 
fine-grained, absorb least water, and are of greatest specific 

fravity, are also most durable under ordinary exposures, 
'he weight of a stone, however, may arise from a large pro- 
portion of metalic oxide — a circumstance often unfavorable 
to its durability. 

The various chemical combinations of iron, potash, and 
alumina, when found in considerable quantities in. the sili- 
cious rocks, greatly affect their durability. The decompo- 
sition of the feldspar in which a considerable portion of the 
silica is removed when the potash dissolves, leaves an excess 
of aluminous matter behind. The clay often absorbs water, 
becomes soft, and causes the stone to crumble to pieces. 

32. Frost, or rather the alternate actions of freezing and 
thawing, is the most destructive agent of nature with which 
the engineer has to contend. Its effects vary with the tex- 
ture of stones ; those of a fissile nature usually split, while 
the more porous kinds disintegrate, or exfoliate at the surface. 
When stone from a new quarry is to be tried, the best indi- 
cation of its resistance to frost may be obtained from an ex- 
amination of any rocks of the same kind, within its vicinity, 
which are known to have been exposed for a long period. 
Submitting the stone fresh from the quarry to the direct 
action of freezing would seem to be the best test of it, if it 
were not that some stones, which are much affected by frost 
when first quarried, splitting under its action, become imper- 
vious to it after they have lost the moisture of the quarry, as 
they do not reabsorb near as large an amount as they bring 
from the quarry. 



16 CIVIL ENGINEERING. 

A test for ascertaining the probable effects of frost on 
stone was invented by M. Brard, a French chemist, which can 
be used for determining the probable comparative durabili- 
ties of specimens. It is to imitate the disintegrating action 
of frost by means of crystallization of sodium sulphate. The 
process may be stated briefly as follows : Let a cubical block, 
about two inches on the edge, be carefully sawed from the 
stone to be tested. A cold saturated solution of the sodium 
sulphate is prepared, placed over a fire, and brought to the 
boiling-point. The stone, having been weighed, is suspended 
from a string, and immersed in the boiling liquid for thirty 
minutes. It is then carefully withdrawn, the liquid is de- 
canted free from sediment into a flat vessel, and the stone is 
suspended over it in a cool cellar. An efflorescence of the 
salt soon makes its appearance on the stone, when it must be 
again dipped in the liquid. This should be frequently done 
during the day, and the process be continued for about a 
week. The earthy sediment found at the end of this period 
in the vessel is carefully weighed, and its quantity will give 
an indication of the like effect of frost. This progress is 
given in detail in Vol. XXXVIII. Annates de Chemie et de 
jPhysique. 

This test, having corresponded closely with their experi- 
ence, has received the approval of many French architects 
and engineers. Experiments, however, made by English engi- 
neers on some of the more porous stones, by exposing them 
to the alternate action of freezing and thawing, gave results 
very different from those obtained by Erard's method. 

33. The Wear of Stone from ordinary exposure is very 
variable, depending not only upon the texture and constituent 
elements of the stone, but also upon the locality, and the posi- 
tion, it may occupy in a structure, with respect to the pre- 
vailing driving rains. This influence of locality on the 
durability of stone is very marked. Stone is observed to wear 
more rapidly in cities than in the country, and exhibits signs 
of decay soonest in those parts of a building exposed to the 
prevailing winds and rains. 

The disintegration of the stratified stones placed in a wall 
is materially affected by the position of the strata or lamina) 
with respect to the exposed surface, proceeding faster when 
the laces of the strata, are exposed, as is the case when the 
stones are not placed with their lamina king horizontally. 

Stones are often exposed to the action o[' high temperatures, 

as in the ease of great conflagrations. They are also used to 
protect portions of a building from great heat, and sometimes 

to line furnaces. Those that resist a high, degree of heat are 






STONE. 17 

I 

termed fire-stones. A good fire-stone should be infusible, 
and not liable to crack or exfoliate from heat. Stones that 
contain lime or magnesia, easssptJa ^hc f o i in uf silicate , are 
usually unsuitable. Also, silicates containing an oxide of 
.iron should be rejected. 

TVTheir durability under such circumstances should be con- 
sidered when selecting them for building. 

The only sure test, however, of the durability of any kind 
of stone is its wear, as shown by experience. 

34. Expansion of Stone from Heat. — Experiments have 
been made in this country and Great Britain to ascertain the 
expansion for every degree of Fahrenheit, and the results 
have been tabulated, within the ordinary ranges of tem- 
perature the stone is too slightly affected by expansion or 
contraction to cause any perceptible change. Professor 
JBartlett's experiments, however, showed that in a long line of 
coping the expansion was sufficiently great to crush mortar 
between the blocks. 

35. Preservation of Stone.— To add to their durabilit} T , 
especially of those stones naturally perishable or showing 
signs of decay, various processes have been tried or proposed. 
All have the same end in view, which is to fill the exposed 
pores of the stone with some substance which shall exclude 
the air and moisture. Paints and oils are used for this pur- 
pose. Great results have been expected from the use of 
soluble glass (silicate of potash), and also from silicate of 
lime. The former, being applied in a state of solution in 
water, gradually hardens, partly through the evaporation of 
its water, and partly through the removal of the potash by 
the carbonic acid in the air. The latter is used by filling the 
pores with a solution of silicate of potash, and then introdu- 
cing a solution of calcium chloride or lime nitrate ; the chemi- 
cal action produces silicate of lime, filling the pores of the 
natural stone. Time and experience will show if the hopes 
expected from the use of these silicates will be realized. 

36. Ease of Working the Stone. — This property is to a 
certain extent the inverse of the others. The ease with which 
stone can be cut or hammered into shape implies either soft- 
ness or else a low degree of cohesiveness between its particles. 

It often happens that its hardness may prevent a stone, in 
every other way suitable, from being wrought to a true sur- 
face and from receiving a smooth edge at the angles. More- 
over, the difficulty of working it will increase very materially 
the cost of the finished stone. 

It requires experience and good judgment to strike a me- 
dium between these conflicting qualities. 
2 



18 CIVIL ENGINEERING. 

37. Quarrying. — If the engineer should be obliged to get 
out his own stone and open a new quarry, he should pay par- 
ticular attention to the best and cheapest method of getting it 
out and hauling it to the point where it is to be used. In all 
cases he will, if possible, open the quarry on the side of a 
hill, and arrange the roads in and leading to it with gentle 
slopes, so as to assist the draught of the animals employed. 
The stone near the surface, not being as good as that beneath, 
is generally discarded. The mass or bed of stone being ex- 
posed, a close inspection will discover the natural joints or 
fissures along which the blocks will easily part from each 
other. When natural fissures do not exist, or smaller blocks 
are required, a line of holes is drilled at short regular inter- 
vals, or grooves are cut in the upper surface of a bed. Then 
blunt steel wedges or pins, slightly larger than the holes, are 
inserted, and are struck sharply and simultaneously with ham- 
mers until the block splits off from the layer. 

If large masses of stone be required, resort is had to blast- 
ing. This operation consists in boring the requisite number 
of holes, loading them with an explosive compound, and fir- 
ing them. The success of blasting will depend upon a judi- 
cious selection of the position and depth of the holes and the 
use of the proper charges. 

Instead of trusting, as is too often done, to an empirical 
rule, or to no rule at all, it is well, by actual experiments on 
the particular rock to be quarried, to ascertain the effect of 
different charges, so as to determine the amount required in 
any case, to produce the best result. 



VARIETIES OF BUILDING STONES IN GENERAL USE. 
SILICIOUS STONES. 

38. Silieious Stones are those in which silica is the prin- 
cipal constituent. With a few exceptions, their structure is 
crystalline-granular, the grains being hard and durable. They 
emit sparks when struck with a steel, and do not generally 
effervesce with acids. 

Some of the principal silieious stones used in building are 
Syenite, Granite, Gneiss, Mica Slate, Hornblende Slate, 
Steatite, and the Sandstones. For their composition, partic- 
ular description, etc. sec any of the manuals of mineralogy. 

Syenite, Granite, and Gneiss. — These Btones differ but lit- 
tle in the qualities essential to a good building material, and 



SILICIOUS STONES. 19 

» 

from the great resemblance of their external characters and 
physical properties are generally known to builders by the 
common term granite. 

- Granite {Syenite, Granite, and Gneiss). — This stone ranks 
high as building material, in consequence of its superior 
strength, hardness, and durability, and furnishes a material par- 
ticularly suitable for structures which require great strength. 
It does not resist well very high temperatures, and its great 
hardness requires practised stone-cutters to be employed in 
working it into proper shapes. It is principally used in works 
of magnitude and importance, as light-houses, sea-walls, 
revetment-walls of fortifications, large public buildings, etc. 
Only in districts where it abounds is it used for ordinary 
dwelling-houses. It was much used by the ancients, especially 
by the Egyptians, some of whose structures, as far as the stone 
is concerned, are still remaining in good condition, aftei\3,000 
years' exposure. Granite occurs in extensive beds, and may 
be obtained from the quarries in blocks of almost any size re- 
quired. Gneiss, in particular, having the mica more in layers, 
presents more of a stratified appearance, and admits of being 
broken out into thin slabs or blocks. A granite selected for 
building purposes should have a fine grain, even texture, and 
its constituents uniformly disseminated through the mass. It 
should be free from pyrites or any iron ore, which will rust 
and deface, if not destroy the stone on exposure to the weath- 
er. The feldspathic varieties are the best, and the sy-enitic 
are the most durable. An examination of the rock in and 
around the quarry may give some idea of its durability. 

Mica Slate has in its composition the same materials as 
gneiss, and breaks with a glistening or shining surface. The 
compact varieties are much used for nagging, for door and 
hearth stones, and for lining furnaces, as they can be broken 
out in thin, even slabs. It is often used in ordinary masonry 
work, in districts where it abounds. 

Hornblende Slate resembles mica slate, but is tougher, and 
is an excellent material for flagging. 

Steatite, or Soapstone, is a soft stone easily cut by a knife, 
and greasy to the touch. From the ease with which it is 
worked, and from its refractory nature, it is used for fire-stones 
in furnaces and stoves, and for jambs in fire-places. Being 
soft, it is not suitable for ordinary building purposes. 

Sandstone is a stratified rock, consisting of grains of silicious 
sand, arising from the disintegration of silicious stones, ce- 
mented together by some material, generally a compound of 
silica, alumina, and lime. It has a harsh feel, and every dull 
shade of color from white, through yellow, red, and brown, to 



20 



CIVIL ENGINEERING. 



pearly a black. Its strength, hardness, and durability vary 
between very wide limits ; some varieties being little inferior 
to good granite as a building-stone, others being very soft, 
friable, and disintegrating rapidly when exposed to the weath- 
er. The least durable sand-stones are those w r hich contain the 
most argillaceous matter ; those of a feldspathic character also 
are found to withstand poorly the action of the weather. The 
best sandstone lies in thick strata, from which it can be cut in 
blocks that show very faint traces of stratification; that which 
is easily split into thin layers, is weaker. It should be firm in 
texture, not liable to peel off when exposed, and should be free 
from pyrites or iron-sand, as they rust and disfigure the blocks. 
It is generally porous and capable of absorbing much water, 
but it is comparatively little injured by moisture, unless when 
built with its layers set on edge. In this case the expansion of 
water between the layers in freezing makes them split or 
" scale " off. It should be placed w T ith the strata in a horizon- 
tal position, so that any water which may penetrate between 
the layers may have room to expand or escape. Most of the 
varieties of sandstone yield readily under the chisel and saw, 
and split evenly; from these properties it has received from 
workmen the name of free-stone. It is used very exten- 
sively as a building-stone, for flagging, for road material; and 
some of its varieties furnish an excellent lire-stone. 

Other varieties of silicious stones besides those named, as 
porphyry, trap or greenstone, basalt, quartz-rook 
(cobble-stone), buhr-stone, etc., are used for building and 
engineering purposes, and are eminently fit, either as cut- 
stone or rubble, as far as strength and durability are concerned. 



ARGILLACEOUS STONES. 



39. Argillaceous or Clayey Stones are those in which 
alumina exists in sufficient quantity to give the stone its charac- 
teristic properties. As a rule, the natural argillaceous stones, 
excepting roofing slate, are deficient in the properties of hard- 
ness and durability, and are unfit for use in engineering con- 
structions. 

Roofing Slate is a stratified rock of great hardness and 
density, commonly of a dark dull blue or purplish color. To 
be a good materia] For roofing, it should split easily into ('vcn 
slates, and admit of being pierced lor nails without being 
fractured. It should be free ('mm everything that can on ex- 
posure undergo decomposition. The signs of good quality in 

slate -are compactness, smoothness, uniformity of texture, clear 



CALCAREOUS STONES. 21 

dark color; it should give a ringing sound when struck, and 
should absorb but little water. Being nearly impervious to 
water, it is principally used for covering of roofs, linings of 
water-tanks, and for other similar purposes. 



CALCAREOUS STONES. 

4:0. Calcareous Stones are those in which lime (calcium 
monoxide) is the principal constituent. It enters either as a 
sulphate or carbonate. 

Calcium Sulphate, known as gypsum in its natural 
state, when burnt and reduced to a powder, is known as 
plaster-of-Paris. A paste made of this powder and a little 
water, becomes, on drying, hard and compact. Gypsum is not 
used as a building-stone, being too soft. The plaster, owing 
to its snowy whiteness and fine texture, is used for taking casts, 
making models, and for giving a hard finish to walls. Care 
must be taken to use it only in dry and protected situations, 
as it absorbs moisture freely, then swells, cracks, and exfoliates 
rapidly. 

Calcium Carbonates, or Limestones, furnish a large 
amount of ordinary building-stone, ornamental stone, and form 
the source of the principal ingredient of cements and mortars. 

They are distinguished by being easily scratched with a 
knife, and by effervescing with an acid. In texture they are 
either compact or granular, in the former case the fracture is 
smooth, often conchoidal ; in the latter it has a crystalline- 
granular surface, the fine varieties resembling loaf-sugar. 

The limestones are generally impure carbonates, and we 
are indebted to their impurities for some of the most beauti- 
ful as well as the most invaluable materials used for construc- 
tions. Those stones which are colored by metallic oxides, or 
by the presence of other minerals, furnish the numerous color- 
ed and variegated marbles ; while those which contain a cer- 
tain proportion of impurities as silica, alumina, etc., yield, on 
calcination, those cements which, from possessing the prop- 
erty of hardening under water, have received the names of 
hydraulic lime, hydraulic cement, etc. 

As a building material, limestones are classed into two 
divisions — those that can receive a polish, and those that can 
not — known respectively as marbles and common lime- 
stone. 

41. Marbles. — Owing to the high polish of which they are 
susceptible, and their consequent value, the marbles are most- 
ly reserved for ornamental purposes. 



22 CIVIL ENGINEERING. 

They present great variety, both in color and appearance, 
and the different kinds have generally received some appro- 
priate name descriptive of these accidents. 

Statuary Marble is of the purest white, finest grain, and 
is free from all foreign minerals. It receives a delicate 
polish, without glare, and is, therefore, admirably adapted to 
the purposes of the sculptor, for whose uses it is mostly 
reserved. 

Conglomerate Marble. — This consists of two varieties; 
the one termed pudding- stone, composed of rounded pebbles 
embedded in compact limestone; the other termed breccia, 
consisting of angular fragments united in a similar manner. 
The colors of these marbles are generally variegated, forming 
a very handsome ornamental material. 

Bird's-eye Marble. — The name of this stone is descriptive 
of its appearance after sawing or splitting, the eyes arising 
from the cross-sections of a peculiar fossil (fucoides demissus) 
contained in the mass. 

Lumachella Marble. — This is obtained from a limestone 
having shells embedded in it, and takes its name from this 
circumstance. 

Verd. Antique. — This is a rare and costly variety, of a 
beautiful green color, caused by veins and blotches of ser- 
pentine diffused through the limestone. 

There are many other varieties that receive their name 
either from their appearance or the localities from which 
they are obtained. 

Many of these are imitated by dealers, who, by processes 
known to themselves, stain the common marbles so success- 
fully that it requires a close examination to distinguish the 
false from the real. 

COMMON LIMESTONE. 

42. This class furnishes a great variety of building- stones, 
which present great diversity in their physical properties. 
Some of them seem as durable as the best silicious stones, and 
are but little inferior to them in strength and hardness ; others 
decompose rapidly on exposure to the weather ; and some 
kinds are so soft that, when first quarried, they can be 
scratched with the nail and broken between the lingers. The 
durability of limestones is materially affected by the foreign 
minerals they may contain ; the presence of clay injures the 
stone for building purposes, particularly when, as sometimes 
happens, it runs through the bed in very minute veins; 

blocks of stone having this imperfection soon separate along 



BRICK. 23 

these veins on exposure to moisture. Ferrous oxide, sulphate 
and carbonate of iron, when present, are also very destructive 
in their effects, frequently causing by their chemical changes 
rapid disintegration. 

Among the varieties of impure carbonates of lime are the 
magnesian limestones, called dolomites. They are re- 
garded in Europe as a superior building material ; those being 
considered the best which are most crystalline, and are com- 
posed of nearly equal proportions of the carbonates of lime 
and magnesia. The magnesian limestone obtained from 
quarries in New York and Massachusetts is not of such good 
quality ; the stone obtained being, in some cases, extremely 
friable. 



II.— ARTIFICIAL STONES. 
1st. — BRICK. 

43. A brick is an artificial stone, made by moulding tem- 
pered clay into a form of the requisite shape and size, and 
hardening it, either by baking in the sun or by burning in a 
kiln or other contrivance. When hardened by the first pro- 
cess, they are known as sun-dried, and by the latter as burnt- 
brick, or simply brick. 

44. Sun-dried Brick. — Sun-dried bricks have been in use 
from the remotest antiquity, having been found in the ruins 
of ancient Babylon. They were used by the Greeks and 
Romans, and especially by the Egyptians. At present they 
are seldom employed. 

They were ordinarily made in the spring or autumn, as 
they dried more uniformly during those seasons ; those made 
in the summer, drying too rapidly on the exterior, were apt 
to crack from subsequent contraction in the interior. 

It was not customary to use them until two years after they 
had been made. 

Walls, known as adobes, made of earth hardened in a simi- 
lar way, are found in parts of our country and in Mexico. 
They furnish a simple and economical mode of construction 
where the weights to be supported are moderate, and where 
fuel is very scarce and expensive. This mode, however suit- 
able for a southern, is not fit for our climate. 

45. Burnt Brick. — Bricks may be either common or 
pressed, hand or machine made. 

The qualities of a brick are dependent upon the kind of 



$Yl * ¥ 



^h 



dk 



24 CIVIL ENGINEERING. 

earth used, the tempering of this earth, the moulding of the 
raw brick, and the drying and burning processes. 

46. Common Brick. — The size and form of common bricks 
vary but little. They are generally rectangular parallelopi- 
pedons, about 9 inches long, 4J inches broad, and 3 inches 
thick, the exact size varying with the contraction of the clay. 

Kinds of Earth. — The argillaceous earths suitable for 
brick-making may be divided into three principal classes, viz. : 

Pure Clays, those composed chiefly of aluminum silicate, 
or one part of alumina and two of silica, combined with a 
small proportion of other substances, as lime, soda, magnesia, 
ferrous oxide, etc.; 

Loams, which are mechanical mixtures of clay and sand ; 
and 

Marls, which are mechanical mixtures of clay and car- 
bonate of lime. 

Pure clay, being made plastic with water, may be moulded 
into any shape, but will shrink and crack in drying, however 
carefully and slowly the operation be conducted. By mixing 
a given quantity of sand with it, these defects may be greatly 
remedied, while the plastic quality of the clay will not be 
materially affected. 

The loams oftentimes have too much sand, and are then so 
loose as to require an addition of clay or other plastic mate- 
rial to increase theii* tenacity. 

Earth is frequently found containing the proper proportions 
of clay and sand suitable for making bricks ; but, if it be not 
naturally fit for the purpose, it should be made so by adding 
that element which is lacking. The proportion of sand or 
clay to be added should be determined by direct experiments. 

Silicate 'of lime, if in any considerable quantity in the 
earth, makes it too fusible. Carbonate of lime, if present 
in any considerable quantity in the earth, would render it 
unfit, since the carbonate, being converted, during t}ie burn- 
ing, into lime, which absorbs moisture upon being exposed, 
would cause disintegration in the brick. 

Preparation of the Earth. — The earth being of the proper 
kind, it is first dug out before the cold weather, and earned 
to a place prepared to receive it. It is there piled into heaps 
and exposed to the weather during the winter, so as to be 
mellowed by the frosts, which break up and crumble the 
luni|w. 

In the spring the earth is turned over with shovels, and the 
stones, pebbles, and gravel are removed ; if either clay 01 
sand be wanting, the proper amount is added. 

Tempering. — The object of tempering is to bring the earth 



BEICK. 25 

into a homogeneous paste for the use of the moulder. This 
is effected by mixing it with about half its volume of water, 
and stirring it and kneading it either by turning it over re- 
peatedly with shovels and treading it over by horses or men 
until the required plasticity is obtained, or by using the pug- 
mill or a similar machine. 

The plastic mass is then moulded into the proper forms by 
hand or machinery. 

By Hand. — In the process by hand the mould used is a 
kind of box, without top or bottom, and the tempered clay is 
dashed into it with sufficient force to completely fill it, the 
superfluous clay being removed by striking it with a straight- 
edge. The newly-made brick is then turned out on a drying- 
floor, or on a board and carried to the place w T here it is to 
dry. 

47. By Machines. — Bricks are now generally moulded by 
machines. These machines combine the pug-mill with an 
apparatus for moulding. This apparatus receives the clay as 
discharged from the pug-mill, presses it in moulds, and pushes 
the brick out in front, ready to be removed from the frames 
and carried to the drying-floor. 

48. Drying-. — Great attention is necessary in this part of 
the process of manufacture. The raw bricks are dried in the 
open air or in a drying-house, wdiere they are spread out on 
the ground or floor, and are frequently turned over until they 
are sufficiently hard to be handled without injury. They are 
then piled into stacks under cover for further drying. 

In drying bricks, the main points to be observed are to pro- 
tect them from the direct action of the sun, from draughts of 
air, from rain and frost, and to have each brick dry uni- 
formly from the exterior inwards. The time allowed for dry- 
ing depends upon the climate, the season of the year, and the 
weather. 

49. Burning. — The next stage of manufacture is the burn- 
ing. The bricks are arranged in the kiln so as to allow the 
passage of the heat around them ; this is effected by piling 
the bricks so that a space is left around each. This arrange- 
ment of the bricks, called setting the kiln, is to allow the heat 
to be diffused equally throughout, to afford a good draught, 
and to keep up a steady heat with the least amount of fuel. 

A very moderate fire is next applied under the arches of 
the kiln to expel any remaining, moisture from the raw brick; 
this is continued until the smoke from the kiln is no longer 
black. The fire is then increased until the bricks of the 
arches attain a white heat ; it is then allowed to abate in some 
degree, in order to prevent complete vitrification ; and it is 



26 CIVIL ENGINEERING. 

thus alternately raised and lowered until the burning is com- 
plete, as ascertained by examining the bricks at the top of the 
kiln. The bricks should be slowly cooled ; otherwise they 
will not withstand the effects of the weather. The cooling is 
done by closing the mouths of the arches and the top and 
sides of the kiln, in the most effectual manner, with moist clay 
and burnt brick, and by allowing the kiln to remain in this 
state until the heat has subsided. The length of time of burn- 
ing varies, but is often fifteen days or thereabouts. 

50. General Qualities and Uses. — Bricks, when properly 
burnt, acquire a degree of hardness and durability that ren- 
ders them suitable for nearly all the purposes to which stone 
is applicable ; for, when carefully made, they are in strength, 
hardness, and durability but little inferior to the ordinary 
kinds of building-stone. They remain unchanged under the 
extremes of temperature, resist the action of water, set firmly 
and promptly with mortar, and, being both cheaper and 
lighter than stone, are preferable to it for many kinds of 
structures, as for the walls of houses, small arches, etc. 

The Romans employed bricks in the greater part of their 
constructions. The scarcity of stone in Holland and the 
Netherlands led to their extensive use, not only in private 
but in their public buildings, and these countries abound 
in fine specimens of brick- work. 

51. Characteristics of good Bricks. — Good bricks should 
be regular in shape, with plane surfaces and sharp edges ; 
the opposite faces should be parallel, and adjacent faces per- 
pendicular to each other. 

They should be free from cracks and flaws ; be hard ; 
possess a regular form, and uniform size ; and, where exposed 
to great heat, infusibility. 

They should give a clear, ringing sound when struck ; and 
when broken across, they should show a fine, compact, uni- 
form texture, free from air-bubbles and cracks. 

They should not absorb more than ^ of their weight of water. 

52. From the nature of the process of burning, it will be 
evident that in the same kiln must be found bricks of very 
different qualities. There will be at least three varieties: 1, 
bricks which are burned too much ; 2, those, just enough ; and, 
8, those, not enough. The bricks forming the arches and ad- 
jacent to the latter, being nearer the fire, will be burnt to 
great hardness, or perhaps vitrified ; those in the interior will 
Be well burnt; and (hose on top and near the exterior will 
1)0 under-burned. The first arc called arch brick ; the sec- 
ond, body, hard, or, if the clay had contained ferrous-oxide, 
cherry red; and the third, soft, pale, or sammel brick. 



TILES. 27 

The arch bricks are very hard but brittle, and have but 
slight adhesion with mortar; the sof t or sammel, if exposed 
to the weather, have not requisite strength nor durability, 
and can, therefore, be used only for inside work. 

53. Pressed Brick. — Pressed brick are made by putting 
the raw bricks, when nearly dry, into moulds of proper 
shape, and submitting them to a heavy pressure by machinery. 
They are heavier than the common brick. All machine- 
made bricks partake somewhat of the nature of pressed 
brick. 

54. Fire-bricks. — Fire-bricks are made of refractory clay 
containing no lime or alkaline matter which remains un- 
changed by a degree of heat that would vitrify and destroy 
common brick. They are haked rather than burnt, and their 
quality depends upon the fineness to which the clay has been 
ground and the degree of heat used in making them. 

They are used for facing fireplaces, lining furnaces, and 
wherever a high degree of temperature is to be sustained. 

Bricks light enough to float in water were known to the 
ancients. During the latter part of the last century M. Fab- 
broni, of Italy, succeeded in making floating bricks of a ma- 
terial known as agaric mineral, a kind of calcareous tufa, 
called fossil meal. Their weight was only one-sixth that of 
common brick ; they were not affected by the highest tem- 
perature, and were bad conductors of heat. 

55. Brick-making was introduced into England by the 
Romans, and arrived at great perfection during the reign of 
Henry VIII. * . 

The art of brick-making is now a distinct branch of the 
useful arts, and the number of bricks annually made in this 
country is very great, amounting to thousands of millions. 

The art of brick-making does not belong to that of the en- 
gineer. But as the engineer may, under peculiar circum- 
stances, be obliged to manufacture brick, the foregoing out- 
line has been given. 

TILES. 

56. Tiles are a variety of brick, and from their various 
uses are divided into three classes, viz. : roofing, paving, and 
draining tiles. 

Their manufacture is very similar to that of brick, the 
principal differences arising from their thinness. This re- 
quires the clay to be stronger and purer, and greater care to 
be taken in their manufacture. 

Their names explain their use. 



28 CIVIL ENGINEERING-. 



2d. CONCRETES. 



57. Concrete is the term applied to any mixture of mortar. .. 
with coarse solid materials, as gravel, pebbles, shells, or frag- 
ments of brick, tile, or stone. 

The term concrete was formerly, applied to the mixture 
made with common lime mortar ; beton, to the mixture when 
the mortar used was hydraulic, i. e., will harden under water. 

The proportions of mortar and coarse materials are de- 
termined by the following principle : that the volume of 
cementing substance should always be slightly in excess of the 
volume of voids of the coarse materials to be united. This 
excess is added as a precaution against imperfect manipula- 
tion. 

Concrete is mixed by hand or by machinery. 

One method, by hand, used at Fort Warren, Boston Harbor, 
was as follows : The concrete was prepared by first spread- 
ing out the gravel on a platform of rough boards, in a layer 
from eight to twelve inches thick, the smaller pebbles at the 
bottom and the larger on the top, and then spreading the 
mortar over it as uniformly as possible. The materials were 
then mixed by four men, two with shovels and two with hoes, 
the former facing each other, always working from the out- 
side of the heap to the centre, then stepping back, and recom-' 
mencing in the same way, and continuing the operation until 
the whole mass was turned. The men with hoes worked each 
in conjunction with a shoveller, and were required to rub well 
into the mortar each shovelful as it was turned and spread. 
The heap was turned over a second time, this having been 
usually sufficient to make the mixture complete, to cover the 
entire surface of each pebble with mortar, and to leave the 
mass of concrete ready for use. 

Various machines have been devised to effect the thorough 
mixing of the materials. A pug-mill, a cylinder in an in- 
clined position revolving around its axis, a cubical box revolv- 
ing eccentrically, and various other machines, have been used. 

58. Uses of Concrete. — Concrete has been generally used 
in confined situations, as foundations, or as a backing for mas- 
sive walls. For many years it has been extensively employed 
in the construction of the public works throughout the united 
States, and is now extended in its application, not only to 
foundations, but even to the building 01 exterior and pail it ion 
walls in private buildings. It has of reeenl years bad <|iiite 
an extensive application in harbor improvements in Europe. 
There are evidences of its extensive use in ancienl times 



PATENT STONES. 'ZV 

in Rome; many public 'buildings, palaces, theatres, aqueducts, 
etc., being built of this material. It has been asserted that 
the pyramids of Egypt are built of artificial stone composed 
of small stone and mortar. , 

It is especially suitable as a building material when dryness, 
water-tightness, and security against vermin are of conse- 
quence, as in cellars of dwelling-houses, magazines on the 
ground or underneath for storage of provisions, etc. 

59. Remarks. — In order to obtain uniformly a good con- 
crete by the use of hydraulic lime or cement, or both, it is 
essential — 

1. That the amount of water be just sufficient to form the 
cementing material into a viscous paste, and that it be sys : 
tematically applied ; 

2. That each grain of sand or gravel be entirely covered 
with a thin coating of this paste ; and 

3. That the grains be brought into close and intimate con- 
tact with each other. 

These conditions require more than the ordinary methods 
and machinery used in making mortars, especially if a supe- 
rior article be desired. 



PATENT STONES. 

60. Various attempts from time to time have been made to 
make an imitation which, possessing all the merits and being 
free from the defects, of the most useful building-stones, 
would supplement, if not supersede, them. These imitations 
are generally artificial sandstones. 



• BETON AGGLOMERE, OR COIGNET-BETON. 

61. Beton agglomere, or coign et-beton, is the name used 
to designate the artificial sandstone which has resulted 
from the experiments and researches of M. Francis Coignet, 
of Paris. 

Manufacture. — The hydraulic lime or cement in powder, 
together with about one-third of its volume of water, are put 
into a suitable mill acting by compression and friction, and 
are subjected to a thorough and prolonged mixing until a 
particular kind of sticky paste is obtained. The excellence 
of the be ton depends greatly on this operation. If too much 
water be used, the mixture cannot be suitably rammed ; if too 
little, it will be deficient in strength. 



30 CIVIL ENGINEERING. 

The sand, deprived of its surplus moisture, and the paste, 
are put in suitable proportions into a ..powerful mill, and 
subjected to a thorough mixing until the compound presents 
the proper appearance, which is, that of a pasty powder. 

The proportions will vary according to the probable uses of 
the stone; 6 volumes of sand to 1 of hydraulic lime in 
powder, or 5 of sand, 1 of hydraulic lime, and 1 of Portland 
cement, are sometimes used. The materials, being in a state 
of pasty powder, are now ready to be placed in moulds. 
Each grain of sand being coated with the paste, it is essential 
that they be brought in intimate contact with each other. 

This is effected by placing the paste in layers of 1| to 2 
inches thick in strong moulds capable of sustaining a heavy 
pressure, and ramming each layer as it is placed by repeated 
blows of an iron-shod rammer until the stratum of material is 
reduced to about one-third of its original thickness. The 
upper surface is struck with a straight-edge, and smoothed off 
with .a trowel. The mould is turned over on a bed of sand, 
and detached from the block. If the block be small, it may 
be handled after one day; larger pieces should have a longer 
time to harden. 

Be ton agglomere is noted for its strength, hardness, and 
durability, and has had quite an extensive application in 
France ; aqueducts, bridges, sewers, cellars of barracks, etc., 
have been built with it. Patents for making a similar stone 
have been taken out for the United States. 



62. Among other artificial stones that are offered to the 
builder are several bearing the name of Pansome, an English 
engineer. The patent silicious stone, Pansome' s apcenite, and 
Pansome's patent stone, are all artificial sandstones, in which 
the cement is a silicate of lime. They differ mostly in the 
process of making. The patent stone has been made in San 
Francisco and in Chicago, and employed to some extent in 
those cities. 

Principles of Manufacture. — Dry sand and a solution of 
silicate of soda, about a gallon of the silicate to a bushel of 
sand, are thoroughly mixed in a suitable mill, and then 
moulded into any of the forms required. These blocks or 
forms are then saturated by a concentrated solution of calcium 
chloride, which is forced through the moulded mass by exhaus- 
tion of the air, by gravity, or by other suitable means. The 
chemical reactions result in the formation of an insoluble 



ASPHALTIC CONCRETE. 31 

silicate of lime, which firmly unites all the grains of the mass 
into one solid, and a solution of sodiiim chloride (common 
salt). The latter is removed by washing with water. 

Remark. — The artificial stone thus formed is uniform and 
homogeneous in its texture, and said to be free from liability 
to distortion or shrinkage. It is also claimed that it is not 
affected by variations of climate or temperature. 



3D. ASPHALTIC CONCRETE. 

63. Asphaltie Concrete is a concrete in which the solid 
materials are united by mastie, a mixture of powdered lime- 
stone, or similar material, with artificial or natural combina- 
tions of bituminous or resinous substances. 

The manufacture of mastics will be described under the 
head of Uniting. Materials ; the manufactured product may 
be bought in blocks ready for use. 

Asphaltie concrete is made as follows : 

The mastic is broken into small pieces, not more than half 
a pound each, and placed in a caldron, or iron pot, over a fire. 
It is constantly stirred to prevent its burning, and as soon as 
melted there is gradually added two parts of sand to each 
one of the mastic, and the whole mass is constantly stirred 
until the mixture will drop freely from the implement used 
m stirring. 

The ground having been made perfectly firm and smooth, 
covered with ordinary concrete, or otherwise prepared, the 
mixture is applied by pouring it on the surface to be coated, 
taking care to spread it uniformly and evenly throughout. 
A square or rectangular strip is first made, and then a second, 
and so on, until the entire surface is completely covered, and 
the surface of each square smoothed with the float. Before 
it becomes hard a small quantity of fine sand is sifted over it 
and is well rubbed in with a trowel or hand-float. 

The thickness of the coating will depend upon its situation, 
being less for the capping of an arch than for the flooring of 
a room, and the latter less than a hall or pavement where 
many are passing. 

Care is taken* to form a perfect union between edges of 
adjoining squares, and where two or more thicknesses are 
used to make them break joints. 

A mixture of coal tar is frequently used as a substitute for 
mastic. 

Uses. — The principal uses of asphaltie concrete are for pav- 
ing streets, side -walks, floors of cellars, etc. 



CIVIL ENGINEERING. 



GLASS. 



64. Glass is a mixture of various insoluble silicates. Its 
manufacture depends upon the property belonging to the al- 
kaline silicates, when in a state of fusion, of dissolving a 
large quantity of silica. The mixture hardens on cooling, 
and is destitute of crystalline structure. 

Uses. — Glass is extensively used in building, as a roof- 
covering for conservatories, ornamental buildings, railroad 
depots, and other structures for which the greatest possible 
light or the best-looking material is required. Other uses, 
as for windows, sky-lights, doors, etc., are familiar to every 
one. 

65. Glazing is the art of fixing glass in the frames of win- 
dows. The panes are secured with putty, a composition of 
whiting and linseed-oil with sometimes an addition of white 
lead. Large panes should be additionally secured by means 
of small nails or brads. 



CHAPTEE III. 

METALS, 



66. The metals used in engineering constructions are Iron, 
Steel, Copper, Zinc, Tin, Lead, and some of their alloys. 



IKON AND STEEL. 

67. Iron has the most extensive application of all the 
metals used for building purposes. It is obtained from the 
ore by smelting the latter in a blast-furnace. When the fuel 
used is coal, the blast is generally of hot-air ; in this process, 
known as the hot-blast, the air, before being forced into the 
furnace, is heated high enough to melt lead. 

When the metal has fused, it is separated from the other 
substances in the ore, and is allowed to combine with a small 
amount of carbon, from 2 to 5 per cent., forming a com- 
pound known as cast-iron, 

A sufficiency of cast-iron having accumulated in the fur- 



CAST-IKON. 33 

nace, the latter is tapped, and the molten metal running out 
is received in sand in long straight gutters, which have 
numerous side branches. This arrangement is called the sovj 
'And pigs ; hence the name of pig-iron. 

The iron in the pig is in a shape to be sent to market, and 
in suitable condition to be remelted and cast into any re- 
quired form, or to be converted into wrought or malleable 
iron. 

Impurities. — The strength and other good qualities of the 
iron depend mainly on the absence of imjpiorities, and espe- 
cially of those substances known to cause brittleness and weak- 
ness, as sulphur, phosphorus, silicon, calcium, and magnesium. 



CAST-IRON. 

68. Cast-iron is a valuable building material, on account 
of its great strength, hardness, and durability, and the ease 
with which it can be cast or moulded into the best forms for 
the purposes to which it is to be applied 

Varieties of Cast-iron.— Cast-iron is divided into six varie- 
ties, according to their relative hardness. This hardness 
seems to depend upon the proportion and state of carbon in 
the metal, and apparently not so much on the total amount 
of carbon present in the specimen, as on the proportionate 
amounts in the respective states of mechanical mixture and 
of chemical combination. Manufacturers distinguish the 
different varieties by the consecutive whole numbers from 1 
to 6. 

No. 1 is known as gray oast-iron, and No. 6 as white 
cast-iron. They are the two principal varieties. 

Gray Cast-iron, of good quality, is slightly mallea*ble when 
cold, and will yield readily to the action of the file if the 
hard outside coating is removed. It has a brilliant fracture of 
a gray, sometimes bluish gray, color. It is softer and tough- 
er, and melts at a lower temperature, than white iron. 

White Cast-Iron is very brittle, resists the file and chisel, 
and is susceptible of high polish. Its fracture presents a sil- 
very appearance, generally fine-grained and compact. 

The intermediate varieties, as they approach in appear- 
ance to that of No. 1 or No. 6, partake more or less of the 
properties characteristic of the extreme varieties. 

Numbers 2 and 3, as they are designated, are usually con- 
sidered the best for building purposes, as combining strength 
and pliability. 

3 



34: CIVIL ENGINEERING. 



APPEARANCES OF GOOD CAST-IRON. 

69. A medium-sized grain and a close compact texture in- 
dicates a good quality of iron. The color and lustre present- 
ed by the surface of a recent fracture are good indications of 
its quality. A uniform dark-gray color and a high metallic 
lustre are indications of the best and strongest iron. With 
the same color, but less lustre, the iron will be found to be 
softer and weaker. ISTo lustre and a dark and mottled color 
indicate the softest and weakest of the gray varieties. 

Cast-iron, of a light-gray color and high metallic lustre, is 
usually very hard and tenacious. As the color approaches to 
white, and as the metallic changes to a vitreous lustre, hard- 
ness and brittleness of the iron become more marked ; when 
the extremes, a dull or grayish white color and a very high 
vitreous lustre, are attained, the iron is of the hardest and most 
brittle of the white variety. 

70. Test of its Quality. — The quality of cast-iron may be 
tested by striking a smart stroke with a hammer on the edge 
of a casting. If the blow produces a slight indentation, 
without any appearance of fracture, the iron is shown to be 
slightly malleable, and therefore of a good quality ; if, on 
the contrary, the edge is broken, there is an indication of brit- 
tleness in the material, and consequent want of strength. 

71. Strength. — The strength of cast-iron varies with its 
density, and the densit}^ depends upon the temperature of the 
metal when drawn from the furnace, the rate of cooling, the 
head of metal under which the casting is made, and the bulk 
of the casting. 

From the many causes by which the strength of iron may 
be influenced, it is very difficult to judge of the quality of a 
casting by its external characters ; however, a uniform ap- 
pearance of the exterior devoid of marked inequalities of sur- 
face, generally indicates uniform strength ; and large castings 
are generally proportionally weaker than small ones. 



WROUGHT OR MALLEABLE IRON. 

72. Wrought, or Malleable Iron, in its perfect condition, 
is simply pure iron. 

It generally falls short of such condition to a greater; or less 
extent, on account of the presence of the impurities referred 
to in a previous paragraph. It contains ordinarily more than 
one-quarter of one per cent, of carbon. 



WROUGHT-IRON. 35 

It may be made J^y direct reduction of the ore, but it is 
usually made from cast-iron by the process called pud- 
dling. 

Wrought-iron is tough, malleable, ductile and infusible in 
ordinary furnaces. At a white heat it becomes soft enough 
to take any shape under the hammer, and admits of being 
welded. In order to weld two pieces together, each surface 
should be free from oxide. If there be any oxide present, it 
is easily removed by sprinkling a little sand or dust or borax 
over the surfaces to be joined ; either of these forms with the 
rust a fusible compound, which is readily squeezed out by the 
hammering or rolling. 



APPEARANCES OF GOOD WROUGHT-IRON. 

73. The fracture of good wrought-iron should have a clear 
gray color, metallic lustre, and a fibrous appearance. A 
crystalline structure indicates, as a rule, defective wrought- 
iron. Blisters, flaws, and cinder-holes are defects due to bad 
manufacture. 

Strength. — The strength of wrought-iron is very variable, 
as it depends not only on the natural qualities of the metal, 
but also upon the care bestowed in forging, and upon the 
greater or less compression of its fibres when it is rolled or 
hammered into bars. 

Forms. — The principal forms in which wrought-iron is 
sent to market are Bar iron, Round-iron, Hoop and Sheet- 
iron, and Wire. 

Bar-iron comes in long pieces with a rectangular cross- 
section, generally square, and is designated as 1 inch, l-§- inch, 
2 inch, according to its dimensions. It is then cut and worked 
into any shape required. 

Bars receive various other forms of cross-section, depend- 
ing upon the uses that are to be made of them. The most 
common forms are the T, H, I, and L, cross-sections, and 
called T-iron, H iron, etc., from their general resemblance 
to these letters, and one whose section is of this shape, i — >, 
called channel iron. The section like an inverted U is fre- 
quently seen. , 

Round iron comes in a similar form, except the cross-sec- 
tion is circular, and it is known, in the same way, as 1 inch, 2 
inch, etc. 

Hoop and Sheet-iron are modifications of bar-iron, the 
thickness being very small in comparison with the width. 

Corrugated iron is sheet-iron of a modified form, by which 



36 



CIVIL ENGINEERING. 




Fig. 1. 



its strength and stiffness are 
greatly increased. The dis- 
tance between the corruga- 
tions, A B, (Fig. I.) varies, 
being 3, 4, or 5 inches ; the 
depth, B C, being about one- 
fourth A B. 

Iron Wire. — The various sizes of wire might be consid- 
ered as small sizes of round-iron, distinguished by numbers 
depending on the dimensions of cross-section, except that wire 
is Srai^^through circular holes in a metal plate, while round- 
iron is rolled, to obtain the requisite cross-sections. 

The numbers run from to 36 ; No. wire has a diameter 
equal to one-third of an inch, and No. 36 one equal to .004 
of an inch ; the other numbers being contained between 
these, and the whole series being known as the Birmingham 
Wire Gauge. 

A series in which the numbers run from to 40, the ex- 
tremes being nearly the same as that just given, is sometimes 
used. It is known as the American Gauge. 



STEEL. 



74. Steel, the hardest and strongest of the metals, is a 
chemical combination of iron and carbon, standing between 
wrought and cast-iron. 

No sharp dividing line can be drawn between wronght-iron 
and steel, based on the proportions of carbon present in the 
product. The differences in their physical properties are 
largely due to the process of manufacture. Many of the 
properties peculiar to wronght-iron have been found to dis- 
appear upon melting the iron, showing that they were the re- 
sult of the manipulation to which the iron was subjected. 

The term steely-iron, or semi-steel, lias been applied when 
the compound contains less than 0.5 per cent, of carbon ; steel, 
when containing more than this, and less than 2 per cent. ; 
but when 2 per cent, or more is present, the compound is 
termed cast-iron, as before stated. 

• 75. Steel is made from iron by various processes, which 
a re of tw o general classes ; the one in which carbon is added 
to i rial leal Tie iron ; the other in which a part of the carbon is 
abstracted from cast-iron. Like iron, steel is seldom pure, 
but contains other substances which, as a pule, aft'ert it inju- 
riously. There are, however, some foreign substances which, 
introduced into the mass during manufacture, have a bene- 



v^r±zJs- 



STEEL. 37 

ficial effect upon flie steel by increasing its hardness and 
tenacity and making it easier to forge and weld. 

76. Steel used for building purposes is made generally / Jay* 
o no of three proc esses : 

1. By fusion of blister steel in crucibles ; as cast-steel ; 

2. By blowing air through melted cast-iron ; as Bessemer 
steel ; or — 

3. By fusion of cast-iron on the open hearth of a rever- 
beratory furnace, and adding the proper quantities of malle- 
able iron or scrap steel ; as Siemens-Martin steel. 

77. The different kinds of steel are known by names given 
them either from their mode of manufacture, their appear- 
ance, from some characteristic constituent, or from some in- 
ventor's process ; such are German-steel, blister-steel, shear- 
steel, cast-steel, tilted-steel, jpuddled-steel, gramdated-steel, 
Bessemer-steel, etc. 

German-steel is produced direct from certain ores of iron, 
by burning out a portion of the carbon in the cast-iron ob- 
tained from smelting the ore. It is largely manufactured in 
Germany, and is used for files and other tools. It is also 
known as natural steel. 

Blister-steel is made hy a process known as "cementa- 
tion" which produces a direct combination of malleable 
iron and carbon. The bars, after being converted into steel, 
are found covered with blisters, from which the steel takes 
its name. It is brittle, and its fracture presents a crystalline 
appearance. It sometimes receives the name of bar-steel. 

Shear-steel is made by putting bars of blister-steel to- 
gether, heating and welding them under the forge-hammer, 
or between rolls; the product is called "Shear-steel." 
"Double," "Single," or " Half ," from the number of bars 
that have been welded together. It is used for tools. 

Cast-steel, known also as crucible-steel, is made by break- 
ing blistered steel into small pieces, and melting it in close 
crucibles, from which it is poured into iron moulds. The 
resulting ingot is then rolled or hammered into bars. 

Its fracture is of a silvery color, and shows a fine, homoge- 
neous, even, and close grain. It is very brittle, acquires ex- 
treme hardness, and is difficult to weld without a flux. 

This is the finest kind of steel, and the best adapted for 
most purposes in the arts ; but, from its expensiveness, it is 
not much used in building. 

Tilted-steel is made from blistered steel by moderately 
heating the latter and subjecting it to the action of a tilt or 
trip-hammer ; by this means the tenacity and density of the 
steel are increased. 



38 CIVIL ENGINEERING. 

Puddled-steel is made by puddling pig-iron, and stopping 
the process at the instant when the proper proportion of car- 
bon remains. 

Granulated-steel is made by allowing the melted pig-iron 
to fall into water, so that it forms into grains or small lumps ; 
the latter are afterwards treated so as to acquire the proper 
proportion of carbon, and then melted together. 

Bessemer-steel, which takes its name from the inventor of 
the process, is made by direct conversion of cast-iron into 
steel. This conversion is effected either by decarbonizing 
the melted cast-iron until only enough of carbon is left to 
make the required kind of steel, or, by removing all the 
carbon, and then adding to the malleable iron remaining in 
the furnace the necessary proportion of carbon ; the result- 
ing product is then immediately run into large ingots. 

Siemens-Martin steel is another variety of steel obtained 
directly from the cast-iron, and takes its name from the in- 
ventors of the process. In this process, the carbon is not re- 
moved by a blast of atmospheric air, as in the Bessemer pro- 
cess, but by the oxygen of the iron ore or iron scales, etc., 
which is obtained from the escaping gases after combustion. 

In each of the last two processes, the temperature is so 
great as to melt wrought iron with ease. 

There are other kinds of steel, possessing certain character- 
istics peculiar to themselves or claimed for them, but whose 
process of manufacture is not publicly known. 

78. Hardening- and Tempering. Steel is more granular 
than iron, and is much more easily melted, but the great dif- 
ference between them is owing to the capability of steel to 
become extremely hard and elastic when tem/p&red. The 
quality of the steel depends in a great measure on the opera- 
tion of hardening and tempering. 

It is hardened by being heated to a cherry-red color, and 
then being suddenly cooled by being plunged into some cold 
liquid. In this way it is rendered very brittle, and so hard 
as to resist the hardest file. To give elasticity, it is tem- 
pered ; this is done by heating the hardened steel to a cer- 
tain degree, and cooling it quickly ; the different degrees of 
heat will depend upon the use to which the steel is to be put. 

These qualities of hardness and elasticity adapt it for vari- 
ous uses, for which neither cast nor wrought- iron would be 
suitable. 

DUKABILITIY OF IRON AND STEEL. 

70. Constructions in these metals are, like those in wood, 
subject to the same general conditions. They may be ex- 



PROTECTION OF IRON WORK. 39 

posed to the. air in a dry place, or in a damp place, be kept 
alternately wet and dry, or be entirely immersed in fresh or 
salt water. 

Their exposure to the air or moisture, especially if an acid 
be present, is followed by rusting which proceeds with 
rapidity after it once begins. The corrosion is more rapid 
under exposure to alternate wetness and dryness than in 
either of the other cases. 

Cast-iron is usually coated with a film, composed of a sili- 
cate of -fpvvrmq ^xjfl^ produced by the action of the sand of 
the mould on the melted iron ; this film is very durable, and, 
if not injured, the casting will last a long time without 
rusting. 

Iron kept in a constant state of vibration rusts less rapidly 
than in a state of rest. 

Iron completely imbedded in brick-work or masonry is 
preserved from rust, and in cathedrals and other ancient 
buildings it has been found in good condition after six hun- 
dred years. In these cases the iron was probably protected 
by the lime in the mortar, the latter being a good pre- 
servative. 

The rapid deterioration of iron-work when exposed to the 
air and to moisture makes its protection, so as to increase its 
durability, a matter of great importance. 



PROTECTION OF IRON-WORK. 

80. The ordinary method, used to protect iron from rust, 
is to cover its surface with some material that withstands the 
action of the air and moisture, even if it be for a limited time. 

The following are some of the methods : 

By painting. — The surface of the iron is covered with a 
coat of paint. Bed and white lead paints, ochreous or iron 
oxide paints, silicate paints, and bituminous paints, all are 
used. For this purpose, the value of the paint depends 
greatly upon the quality of the oil with which it is mixed. 
The painting must be renewed from time to time. 

By japanning. — The iron being placed in a heated cham- 
ber, or furnace, the paint is there applied, and is to some 
extent absorbed by the iron, forming over it a hard, smooth, 
varnish-like coating. 

By the use of eoal-tar. — The iron is painted with coal-tar 
alone or mixed with turpentine or other substances ; another 
method consists in first heating the iron to about 600° Fahr., 
and then boiling it in the coal-tar. 




40 CIVIL ENGINEERING. 

By the use of linseed oil. — The iron is heated, and the 
surface while hot is smeared over with cold linseed-oil. 

By galvanizing - . — This term, u galvanized iron," is ap- 
plied to articles of iron coated with zinc. The iron, being 
thoroughly cleaned and free from scale, is dipped into a bath 
of melted zinc, and becomes perfectly coated with it. This 
coating protects the iron from direct action of the air and 
moisture, and as long as it lasts intact the iron is perfectly 
free from rust. 

COPPER. 

81. This metal possesses great durability under ordinary 
exposure to the weather, and from its malleability and tena- 
city is easily manufactured into thin sheets and fine wire. 

When used for building purposes, its principal application 
is in roof -coverings, gutters, and leaders, etc. Its great 
expense, compared with the other metals, forms the chief 
objectipn to its use. 

ZINC. 

82. This metal is used much more than copper in building, 
as it is much cheaper and is exceedingly durable. ■ Though 
zinc is subject to oxidation, the oxide does not scale off like 
that of iron, but forms an impervious coating, protecting the 
metal under it from the action of the atmosphere, thus ren- 
dering the use of paint unnecessary. 

I t i s very . duotifc, and can be easily bent into any required ,^ 
shape. 

The expansion and contraction caused by variations of tem- 
perature are greater for zinc than iron, and when zinc is used 
for roof -coverings, particular attention must be paid to seeing 
that plenty of play is allowed in the laps. 

Zinc, before it is made into sheets or other forms, is called 
spelter. 

TIN. 

83. This metal is only used, in building, as a coating for 
sheet-iron or sheet-copper, protecting their surfaces from 
oxidation. 

LEAD. 

84. This metal was at one time much used for roof-cover- 
ing, lining of tanks, etc. It is now almost entirely super- 
set !<■<] by the other metals. 



V 7 / C ( £^WW~otAv 



UNITING MATERIALS. 41 

It possesses durability, but is wanting in tenacity ; this 
requires the use of thicker sheets which increase both the 
expense and the weight of the construction. 



ALLOYS. 

85. An alloy is a compound of two or more metals, 
mixed while in a melted state. Bronze, gun-metal, bell- 
metal, brass, pewter, and the various solders are some 
of the alloys that have a limited application to building pur- 
poses. 



CHAPTER IT. 

UNITING MATERIALS. 



86. Structures composed of wood and iron have their dif- 
ferent portions united principally by means of straps and 
pins made of solid materials ; in some cases, especially in 
the smaller structures, a cementing material^ is used, as glue, 
etc. 

The use of straps, pins, and like methods of fastenings 
will be described under the head of Framing. 

Structures composed of stone have their different portions 
united principally by cementing materials, as limes, cements, 
mortars, etc. 

GLUE. 

87. Glue is a hard, brittle, brownish product obtained by 
boiling to a jelly the skins, hoofs, and other gelatinous parts 
of animals, and then straining and drying it. 

When gently heated with water, it becomes viscid and 
tenacious, and is used as a uniting material. Although pos- 
sessing considerable tenacity, it is so readily impaired by 
moisture that it is seldom used in engineering constructions, 
except for joiner's work. 



42 CIVIL ENGINEERING. 

LIMES AND CEMENTS. 
LIMES. 

88. If a limestone be calcined, the carbonic acid will be 
driven off in the process, and the substance obtained is gen- 
erally known as lime. 

This product will vary in its qualities, depending on the 
amount and quality of the impurities of the limestone. As 
a building material, the products are divided into three prin- 
cipal classes : 

1. Common or fat lime. 

2. Hydraulic lime. 

3. Hydraulic cement. 
Common lime is sometimes called air-lime, because a paste 

made from it with water will harden only in the air. 

Hydraulic lime and cement are also called water limes 
and cements, because a paste made from either of them 
with water has the valuable property of hardening under 
water. 

The principal use of the limes and cements in the engineer's 
art is as an ingredient in the mortars and concretes. 

> 

VARIETIES OF LIMESTONE. 

89. The majority of limestones used for calcination are 
not pure carbonates, but contain various other substances, the 
principal of which are silica, alumina, magnesia, etc. 

If these impurities be present in sufficiently large quan- 
tities, the limestone will yield on calcination a product pos- 
sessing hydraulic properties. 

Limestones are therefore divided into two classes, common 
and hydraulic, according as the product obtained by calcina- 
tion does or does not possess hydraulic properties. 

90. Common Limestone. — A limestone which does not 
contain more than ten per cent, of these impurities, when 
calcined, produces common lime. White chalk, and statu- 
ary marble, are specimens of pure limestone, or carbonate of 
lime. 

91. Hydraulic Limestones. — Limestones containing 
more than ten per cent, of" these impurities are called hy- 
draulic limestones, because they produce, when properly cal- 
cined, a lime having hydraulic properties. 



# 



V' Vi\ t. w* 



**«t&v\ 



HYDRAULIC LIMESTONES. 43 

The hydraulic limestones are subdivided into silieious, 
argillaceous, magnesian and argillo-magnesian, according 
to the nature of the predominating impurity present in the 
stone. 

PHYSICAL CHARACTERS AND TESTS OF HYDRAULIC LLMESTONES. 

92. The simple external characters of a limestone, as color, 
texture, fracture, and taste, are insufficient to enable a person 
to decide whether it belongs to the hydraulic class. 

They are generally of some shade of drab or of gray, or of 
a dark grayish blue ; have a compact texture, even or con- 
choidal fracture, a clayey or earthy smell and taste. Although 
the hydraulic limestones are usually colored, still the stone 
may happen to be white, from the combination of lime with 
a pure clay. 

The difficulty of pronouncing upon the class to which a 
limestone belongs renders necessary a resort to chemical 
analysis and experiment. 

To make a complete chemical analysis of a limestone re- 
quires more skill in chemical manipulations than engineers 
usually possess ; but a person who has the ordinary element- 
ary knowledge of chemistry can ascertain the quantity of 
clay or of magnesia contained in a limestone, and (know- 
ing this) can pronounce, with tolerable certainty, as to the 
probabilities of its possessing hydraulic properties after cal- 
cination. 

Having from the proportions ascertained that the stone will 
probably furnish a lime with hydraulic properties, a sample 
of it should be submitted to experiment. The only apparatus 
required for this purpose is a crucible that will hold about a 
pint, and a mortar and pestle. The bottom as well as the top 
or cover of the crucible should be perforated to give an up- 
ward current of air and allow the carbonic acid to escape. 
The stone to be tested is broken into pieces as nearly the 
same size as possible, not exceeding three-fourths of an inch 
cube, and placed in the crucible. When more than one speci- 
men is to be tried, and a comparison between them made, 
there should be several crucibles. Access being had to an 
anthracite coal-fire in an open grate, or to any other steady 
fire, the crucibles are embedded in and covered with glowing 
coals, so that the top and bottom portions of their contents 
will attain simultaneously a bright- red heat, each crucible 
containing as nearly as possible the same quantity of stone. 
If there be only one crucible, two or three of the fragments 
are removed in forty-five minutes after the stone has 



41 CIVIL ENGINEERING. 

readied a red heat ; in forty-five minutes afterwards two or 
three more are taken out, and this repeated for four and a 
half and perhaps six hours, which time will be sufficient to 
expel all the carbonic acid. If there he several crucibles, 
they themselves may be removed in the same order. By this 
means we will have some samples of the stone that are burnt 
too much, some not enough, and some of a class between 
them. 

The specimen, if a cement, will not slake when sprinkled 
with water. By reducing it to a powder in the mortar, mix- 
ing it to a stiff paste with water, immersing it in fresh or salt 
water, and noting the time of setting and the degree of hard- 
ness it attains, an approximate value of the 'cement may be 
obtained. 

CALCINATION OF. LIMESTONES. 

93. As the object in burning limestone is to drive off the 
water and carbonic acid from the limestone, many devices 
have been used to effect it. A pile of logs burning in the 
open air, on which the limestone or oyster-shells are thrown, 
lias been frequently used to obtain common lime. It is, how- 
ever, generally manufactured by burning the limestone in a 
kiln suitably constructed for the purpose. 

94. Kilns are divided into two classes : 1st, the intermit- 
tent kilns, or those in which the fuel is all at the bottom, 
and the limestone built up over it ; and, 2d, the perpetual 
or draw kiln, in which the fuel and the limestone are 
placed in the kiln in alternate layers. The fuel used is 
either wood or coal. In the first class one charge of lime is 
burned at a time, and, when one burning is complete, the kiln 
is completely cleared out previous to a second ; while in the 
latter class fresh layers of fuel and limestone are added at 
the top as the lime is drawn out at the bottom. 

The shapes given to the interiors of kilns are very different. 
The object sought is to obtain the greatest possible uniform 
heat with the smallest expenditure of fuel, and for this pur- 
pose thick walls are necessary to prevent loss of heat by radi- 
ation. 

95. Intermittent Kilns. — The simplest form of kiln is 
that represented in Fig 2, in which wood is used for fuel. It 
has a circular horizontal cross-section, and is made of ham- 
mered limestone without mortar. 

The cut represents a vertical seelion through the axis and 
arched entrance oommuuicating with the interior of a kiln 
for burning lime with wood ; c, c, c, large pieces of limestone 



LnrE-KILNS. 



45 



forming the arcli upon which the mass of limestone rests ; A, 
arched entrance communicatinir with the interior. 




Fig. 2. 



It is usually placed on the side of a hill, so that the top 
may be accessible for charging the kiln. 

The largest pieces of the limestone to be burned are 
formed into an arch, c, c, o, and above this the kiln is filled 
by throwing the stone in loosely from the top, the largest 
stones first and smaller ones afterwards, heaping them up, as 
shown in the figure. The fuel is supplied through the 
arched entrance, A. 

The circular seems the most suitable form for the horizon- 
tal sections of a kiln, both for strength and for economy of 
heat. Were the section the same throughout, or the form of 
the interior of the kiln cylindrical, the strata of stone, above 
a certain point, would be very imperfectly burned when the 
lower strata were calcined just enough, owing to the rapidity 
with which the inflamed gases arising from the combustion 
are cooled by coming into contact with the stone. To pro- 
cure, therefore, a temperature which shall be nearly uniform 
throughout the heated mass, the horizontal sections of the 
kiln should gradually decrease from the point where the 
flame rises, which is near the top of the dome of broken 
stone, to the top of the kiln. This contraction of the hori- 
zontal section from the bottom upward should not be made 



46 CIVIL ENGINEEEING. 

too rapidly, as the draught would be thereby injured and the 
capacity of the kiln too much diminished ; and in no case 
should the area of the top opening be less than about one- 
fourth the area of the section taken near the top of the dome. 
The proportions between the height and mean horizontal sec- 
tion will depend on the texture of the stone, the size of the 
fragments into which it is broken for burning, and the 
greater or less ease with which it vitrifies. 

A better kiln than the one shown in Fig. 2 will be obtained 
by giving an ovoidal shape to the interior, lining it with fire- 
brick, substituting for the arch of lime-stones a brick one 
with openings to admit a free circulation of air, so as to 
secure the necessary draught, and arranging it with a fire- 
grate. 

The management of the burning is a matter of experience.- 
For the first eight or ten hours the fire should be carefully 
regulated, in order to bring the stone gradually to a red heat. 
By applying a high heat at first, or by any sudden increase 
of it before the mass has reached a nearly uniform tempera- 
ture, the stone is apt to shiver, and to choke the kiln by stop- 
ping the voids between the courses of stone which form the 
dome. After the stone is brought to a red heat, the supply 
of fuel should be uniform until the end of the calcination. 
Complete calcination is generally indicated by the diminu- 
tion which gradually takes place in the mass, and which, at 
this stage, is about one-sixth of the primitive volume ; by 
the broken appearance of the stone which forms the dome, 
and by the interstices being choked up with fragments of 
the burnt stone ; and by the ease with which an iron 
bar may be forced down through the burnt stone in the 
kiln. When these indications of complete calcination are 
observed, the kiln should be closed for ten or twelve hours 
to confine the heat and finish the burning of the upper 
strata. 

The defects of the intermittent kilns are that the stone 
nearest the fire is liable to be injured by over-burning 
before the top portions are burnt enough, and great waste or 
fuel. 

96. Perpetual Kilns. — Perpetual kilns are intended to 
remedy these defects, especially the waste of heat. A simple 
form of a kiln of this class is shown in Figs. 8 and 4. The 
interior is an inverted frustum of a cone from five to five 
and a half feet in diameter at bottom, and nine or ten at 
top, and thirteen or fourteen high. It is arranged with 
three arched entrances, 0, a, a, for drawing the lime, and they 
are arranged with doors for regulating the draught. 



LIME-KILNS. 



17 



Fig. 3 represents a horizontal section made near the base, 
and Fig. 4, a vertical section on A B, through the axis of 
the kiln. 




6' > 




Fig. 3. 



Fig. 4. 



These kilns are arranged for burning by first placing a 
layer of light wood at the bottom, then a layer of coal, and 
then a layer of limestone. Layers of coal and limestone 
follow alternately until the kiln is filled. The lower layer is 
ignited, and as the burnt mass settles down, and the lime 
near the bottom is sufficiently burnt, the drawing com- 
mences. 

Wood is not as convenient a fuel as coal for this kiln, the 
principal objections being the difficulty of obtaining the 
pieces always the same size and of distributing it uniformly 
in the layers. 

The perpetual kiln is more economical than the intermit- 
tent in the use of fuel, but requires more skill and caution 
in its management. 

The perpetual kiln invented by Mr. C. D. Page, of Roches- 
ter, N. Y., is extensively used in the western part of TsTew 
York and iiu Maine. It is known as a perpetual flame 
or furnace kiln, is arranged for either wood or coal, anthra- 
cite or bituminous, and avoids the defects arising from mix- 
ing the fuel and stone together. 

The foregoing are types of the kilns used for burning lime- 
stones, whether the product is to be common lime or hydrau- 
lic cement. The perpetual kiln is generally used for burning 
limestone for cement. 

Figures 5 and 6 represent vertical sections through the 
axis of the kiln and draw-pit of the ordinary perpetual 
kilns used in the United States for burning lime-stone for 
cement. 

Fig. 5 represents the section of the kiln used in Maryland 



48 



CIYIL ENGINEERING. 



and Virginia ; and Fig. 6 of those preferred in New York 
and Ohio. 




Fig. 5. 



Fig. 6. 



97. The great object of a kiln is to give a cement of good 
and homogeneous quality with economy of fuel. This uni- 
formity of product is not obtained from either the intermit- 
tent or perpetual kilns ordinarily used ; some of the stone 
being over-burnt, while other portions, usually the largest 
fragments, are under-burnt, in some cases partly raw inside* 
Both over and under-burnt pieces are difficult to reduce to 
powder, and materially affect the quality of the cement. It 
is very evident that dissimilar stones should not be burned 
together in the same kiln. 

Various kilns have been devised to remedy all defects, and 
still be economical of fuel. The perpetual flame or furnace 
kiln of Page, before named, and the annular or ring kiln, of 
which the Tloffman is a type, are noted examples. 



PRODUCTS OF CALCINATION OF LIMESTONES. 

98. The products obtained by calcination have been divid- 



COMMON AND HYDRAULIC LIMES. 49 

ed into common lime, hydraulic lime, and hydraulic 
cement. 

COMMON LIME. 

99. Lime, common lime, air-lime, quick-lime, caustic 
lime (synonymous terms) is a calcium monoxide, produced 
whenever any variety of pure or nearly pure limestone is 
calcined with a heat of sufficient intensity and duration to 
expel the carbonic acid [carbon dioxide]. It is amorphous, 
infusible, somewhat spongy, highly caustic, has a specific 
gravity of 2.3, and possesses great avidity for water. On 
being mixed with an equivalent of water, the water is rapidly 
absorbed with evolution of great heat ; the lime swells, bursts 
into pieces, and finally crumbles into a fine white powder, of 
which the volume is from two and a half to three and a half 
times that of its original bulk. In this condition the lime is 
said to be slaked and ready for use in making mortar. 

The limestones which furnish the lime of commerce are 
seldom pure, the impurities amounting sometimes to nearly 
ten per cent. The purer the limestone, the larger is the in- 
crease of volume or growth of the lime in slaking, and the 
more unctuous to the sight and touch is the paste made there- 
from. For this reason the limes made from the purer stones 
are often called fat or rich limes, as distinguished from 
those known as poor or meagre limes, and which are made 
from stones containing considerable impurity. 

The poor limes are seldom reduced to an impalpable, ho- 
mogeneous powder by slaking, and are characterized by less 
growth. They yield a thin paste, and are principally used 
as fertilizers. If it be necessary to use them for building 
purposes, they should be reduced to a fine powder by grind- 
ing ; however, they should never be used if it be possible to 
avoid so doing. 

HYDBATTLIC LIMES. 

100. These occupy an intermediate place between the com- 
mon limes and the hydraulic cements. They are obtained by 
calcining limestones in which the impurities, silica, alumina, 
magnesia, etc., range from ten to twenty per cent. When 

•■ from ten to twenty per cent, of tjpfr impurity is clay, and is 
homogeneously mixed with carbonate of lime, they are known 
as argillaceous hydraulic limestones ; and when this propor- 
tion of impurity (nearly) is $£ silica, they are called silicious 
hydraulic limestones. 
4 



50 CIVIL ENGINEERING. 

Hydraulic lime, upon being mixed with water, slakes more 
slowly than the meagre limes, suffers a slight elevation of tem- 
perature accompanied by little or no vapor, and an increase 
of volume rarely exceeding one-third of its original bulk. A 
paste made from this lime after it has been slaked, hardens 
under water. 

It is not manufactured in the United States, nor is it known 
if there be in the United States any deposits of the argilla- 
ceous hydraulic limestones capable of furnishing good hydrau- 
lic lime. 

Hydraulic lime, made from the argillaceous limestone, is 
manufactured in several localities in France, notably at Seilley, 
about seventy miles from Paris. 

The best type of hydraulic lime from the silicious lime- 
stone is that known as the hydraulic lime of Teil, from the 
quarries of Teil on the Rhone, Department of Ardeche, France. 



HYDRAULIC CEMENT. 

101. If the limestone contain more than 20 per cent, and 
less than 40 of the impurities before named, the product ob- 
tained by calcination is an hydraulic cement. 

Hydraulic cement will not slake, and a paste made from it 
with water will harden or set under water. The rapidity of 
setting and the degree of hardness will vary with the homo- 
geneous character of the stone, the proportions into which the 
clay and lime enter, and the intensity and duration of the 
burning. 

The effect of heat on lime-stones varies with the constituent 
elements of the stone. The pure limestones, and those in 
which -the only impurity is not more than 22 per cent, of 
clay, will stand a high degree of temperature, losing their 
carbonic acid and water without fusing, while the others become 
more or less vitrified when the temperature much exceeds a 
red heat. 

102. There are two general classes of hydraulic cements, 
the slow and the quick setting. 

If the limestone contain at least 20, and not more than 22 
per cent, of clay, and is burned at high heat, the product is a 
heavy, slow-setting cement. 

If there be from 27 to 30 per cent, of clay, and even as 
high as 35 in some cases, and the burning be moderate, the 
result is a light, quick-setting cement. 

The stone that might, with proper burning, have yielded a 
slow-setting cement, will, if burned at a moderate heat, pro- 



POZZUOLANAS. 51 

duce a light, quick-setting cement. The Roman cement, that 
of Vassy, and the hydraulic cements ordinarily made in the 
United States, are examples of the quick-setting class. 

The proportion existing between the impurities and the 
lime exercises a controlling influence on the properties of the 
hydraulic cements, and, when the proportion of lime is less 
than 40 per cent., the stone will, upon calcination, produce 
neither lime, hydraulic lime, nor hydraulic cement. 

POZZUOLANAS. 

103. If clay be present in excess in the limestone, the prod- 
uct obtained by calcination is known as calcareous poz- 
zuolana, and when there is 10 per cent, of lime or less, simply 
pozzuolana. 

Pozzuolana, which gives the name to this class, is a kind 
of tufa, of volcanic origin, containing about 9 per cent, of lime, 
45 of silica, 15 of alumina, and the rest of other impurities, 
and is found near Rome, in Italy. 

It was originally discovered at the foot of Mount Vesuvius, 
near the village of Pozzuoli, whence its name. 

It sometimes exists in a coherent form, but more frequently 
in powder of coarse, sharp, and angular grains, generally 
brown in color, running to reddish. If lime be added to 
supply the deficiency, hydraulic properties can be imparted 
to the mortar made from it. This fact has been known for 
centuries, and Vitruvius and Pliny both speak of its high 
qualities and its use by the Romans in the marine construc- 
tions of their time. 

104. Artificial Pozzuolanas. — They may be prepared by 
grinding well-burnt bricks to powder, or by burning brick- 
clay and grinding it. 

TRASS OK TERRAS. 

105. This substance resembles pozzuolana, is used in the 
same manner, and possesses the same properties. It is used 
in Holland, beins; principally obtained from Bonn and An- 
dernach, on the Rhine, below Coblentz. If any deposits exist 
in the United States, they are not known. 

MANUFACTURE OF COMMON LIME. 

106. Common lime is obtained, as already stated, by the cal- 
cination of limestones, in which there is less than ten per cent. 



52 CIVIL ENGINEERING. 

of impurities ; the limestone is burnt in kilns, and in the 
manner already described. 



MANUFACTURE OF HYDRAULIC LIMES. 

107. Hydraulic lime is not manufactured in the United 
States. 

In France it is manufactured by burning in a suitable 
kiln, at a heat sufficient to drive off the carbonic acid. While 
still warm from the kiln, the stone is sprinkled with from 15 
to 20 per cent, of its own weight of water, care being taken 
not to use enough to convert any portion of it into paste. 
The slaking soon begins, and the stone falls to pieces. The 
mass in then thrown together in large heaps, and left undis- 
turbed for six or eight days. It is then screened with sieves 
of 25 to 30 tine wires to the lineal inch. 

The portion which passes the screen is hydraulic lime. 



MANUFACTURE OF HYDRAULIC CEMENTS. 

108. The hydraulic cements produced at a low heat are 
light in weight and quick-setting, and the mortars and con- 
cretes made from them never attain the strength and hard- 
ness of those made from the heavy and slow-setting cements 
produced by burning with heat of great intensity and duration. 



HYDRAULIC CEMENTS FROM ARGILLACEOUS LIMESTONES. 

109. Heavy, Slow-setting Cements.— The best example 
of this class is the Portland cement, which is made from 
argillaceous limestones, containing from 20 to 22 per cent. 
of clay, or from an artificial mixture of carbonate of lime 
and clay- in similar proportions. Nineteen-twentieths of all 
the Portland cement of the present da}' is artificial. It is manu- 
factured extensively throughout Europe, either by the wet 
process, as in England, or the dry process, as in Germany. 



THE WET PROCESS. 

110. The wet process, as practised by the works near 
London, is as follows : The carbonate of lime is furnished by the 



CEMENTS. 53 

chalks, and the clay is from the shores of the Medway and 
Thames and adjoining marshes; both the chalk and clay are 
practically pure. 

First. The clay and chalk in the proper proportions, abont 
one to three by weight, are mixed together in a circular wash- 
mill, so arranged as to thoroughly pulverize the chalk and 
convert the whole into a semi-fluid paste. 

Second. When the thorough mixture is effected, the liquid, 
resembling whitewash in appearance, is drawn off into reser- 
voirs, where it is left to settle. The heavier material, or raw 
cement, settles to the bottom, and then the surplus water which 
is clear is removed. Samples are taken from the reservoirs 
from time to time and tested. If any error be discovered in 
the proportions, it is corrected. 

Third. When by evaporation the mixture has attained the 
consistency of hard butter or stiff clay, it is removed from the 
reservoirs to rooms artificially heated, and is spread out for 
further drying. 

Fourth. After it has dried sufficiently, it is burned in suit- 
able kilns at a white heat, just below the point of vitrif action. 

Fifth. The product is then ground between ordinary mill- 
stones to a powder of the necessary fineness. It is then ready 
for use. 

THE DRY PROCESS. 

111. The dry process, as practised in Germany, is as fol- 
lows : The carbonate of lime and clay are first kiln-dried at the 
temperature of 212° Fahr., then mixed together in the proper 
proportions, between 20 and 23 per cent, of clay to between 
80 and 77 per cent, of the carbonate of lime, and reduced to 
a fine powder. This powder is then made into a stiff paste, 
and then into blocks about the size of bricks. These bricks 
are dried. and then burnt at a high heat in a kiln, and then 
ground to powder as in the preceding case. 

112. It is an easy matter to pulverize the materials, either 
wet or dry, mix them, and then grind the burnt stone to a 
powder. The difficult part is the proper application and 
management of the heat in burning. The mysterious con- 
version which takes place in the kiln under a heat of suffi- 
cient intensity to make glass, is to some extent beyond oar con- 
trol, and to a great extent beyond our knowledge. 

In whatever manner apparently homogeneous limestones 
may be exposed to burning at a high temperature, it is impos- 
sible to avoid the vitrifaction of some layers containing an 



54 CIVIL ENGINEERING. 

excess of silica and to prevent others not having enough clay 
from producing cements having lime in excess. For this rea- 
son an artificial mixture of clay and carbonate of lime is gen- 
erally relied upon for Portland cement. 

The superior quality of Portland cement appears to depend 
greatly upon the presence of the double silicate of lime and 
alumina, which is formed only at a high heat. 

If an argillaceous limestone does not contain at least 20 
per cent, of clay, the carbonate of lime is in excess, and the 
high heat necessary to produce a heavy, slow-setting cement 
fails to produce the semi-fusion which is the characteristic 
of such a cement. 

113. Light, Quick-Setting- Cements. — If the limestone 
contain more than 23 per cent, of clay, as great as 30 per cent, 
and exceptionally as high as 35 per cent., and the calcination 
be kept below the point of vitrifaction, it will yield a light, 
quick-setting cement. The result appears to be silicate and 
aluminate of lime with uncombined clay, but more especially 
silica, which, being inert, adulterates and injures the cement. 

A cement of this kind sets quickly under water, but is far 
inferior to the Portland cement in hardness and final strength. 
Those of Yassy, Grenoble, etc., in France, and the English 
and French Roman cements made from nodules of septaria, 
belong to this class. 

This kind of cement may be made artificially, and was 
quite extensively used before the superior qualities of the 
Portland cement were known. 

If the limestone contain more than 23 per cent, of clay ho- 
mogeneously distributed through the mass, and is burnt with 
a heat of great intensity and duration, similar to that required 
to produce Portland cement, it generally fuses into a species 
of slag or glass, and is worthless as a cement. 

HYDRAULIC CEMENTS FROM ARGILLO-MAGNESIAN LLMESTONES. 

114. The natural hydraulic cements of the United States 
are made from the limestones whose principal ingredients 
are carbonate of lime, carbonate of magnesia, and clay. 

The usual process of manufacture is to break the stone into 
pieces not exceeding twelve or fifteen pounds in weight, and 
burn them in an ordinary kiln, either intermittent or perpet- 
ual, the latter being generally used when coal is the fuel. 
After being burnt, the fragments are crushed by suitable 
machinery, and then reduced to a powder by grinding. The 
powder is then packed in barrels and sent to market. 



CEMENTS. 55 

These limestones cannot be burned with the intensity and 
duration of heat necessary to make Portland cement, without 
fusing into a slag destitute of hydraulic properties. Like 
those argillaceous limestones which have more than 23 per 
cent, of clay, they will, if properly burned, produce a light, 
quick-setting cement, which is a silicate and aluminate of 
lime and magnesia. 

The cements from the valley of Rondout Creek, Ulster 
County, 1ST. Y., known as Rosendale cement ; from near 
Shepherdstown, Ya. ; Cumberland, Md. ; Louisville, Ky. ; 
Sandusky, Ohio ; Utica, 111. ; and other localities in the 
U. S.j are made from this stone, and belong to this class of 
cements. 

The Rosendale cement, which is the most valuable of them, 
will, under favorable circumstances, attain about one-third 
of the ultimate strength, and hardness of the Portland ce- 
ment. 

HYDRAULIC CEMENTS FEOM MAGNESIAN LIMESTONES. 

115. Pure carbonate of magnesia, known as magnesite, 
when burned at a cherry -red heat, reduced to powder, and 
made in a paste, possesses hydraulic properties. If the pow- 
der be mixed in a paste with magnesium chloride — or, a very 
good substitute for it, bittern, the residue of sea-water after 
the salt has been separated by crystallization — a cement is 
made superior in strength and hardness to any other known, 
not excepting even the Portland. This calcined magnesite 
has been patented under the name of Union cement. 

The dolomites, or magnesian limestones, when burned at 
a low heat and reduced to a powder, will give a mortar with 
hydraulic properties ; and in general any magnesian lime- 
stone containing as high as 60 per cent, of carbonate of mag- 
nesia, if properly burned, will yield an hydraulic cement, 
whether clay be present or not. 



116. This is a cement invented by Major Scott, of the 
Royal Engineers, British. Army, and is referred to, not for 
any marked advantages it possesses, but for the peculiarity 
of its mode of manufacture. 

The limestone is calcined in the usual manner, producing 
common lime. It is then, in lavers of one and a half to two 



56 CIVIL ENGINEERING. 

feet thick, laid over the arches of a perforated oven, and 
brought to a dull glow. The fire is then raked out, and iron 
pots containing coarse, un purified sulphur ( about fifteen 
pounds to each cubic yard of lime) are pushed in on the 
grate-bars, and the sulphur iguited. The oven is closed, so 
as to prevent the escape of the sulphurous vapor. After the 
sulphur has been consumed, the mass is allowed to cool, and 
is then ground to a powder like other cements. 

Why lime treated in this manner should acquire hydraulic 
properties is not fully known. 



TESTS FOE LIMES AND CEMENTS. 

117. The manufacture of limes and cements having become 
a special branch of industry in the United States and Europe, 
the engineer can easily obtain the kinds required for his pur- 
poses, and will rarely, if ever, be placed in a position requir- 
ing him to make them. He will be more particularly con- 
cerned in knowing how to test the samples furnished him, so 
as to be able to make a judicious selection. 

Test for Rosendale Cement. — Rosendale cement should 
be ground fine enough so that 90 per cent, of it can pass a No. 30 
wire sieve of thirty-six wires to the lineal inch both ways ; 
should weigh not less than sixty-eight pounds to the struck 
bushel, loosely measured ; and when made into a stiff paste 
without sand, and formed into bars, should, when seven days 
old, sustain, without rupture, a tensile strain of sixty pounds 
to the square inch of cross-section, the sample having been six 
days in water. 

Test for Portland Cement. — Portland cement should pos- 
sess the same degree of fineness as just given ; should weigh 
one hundred and six pounds to the struck bushel, loosely meas- 
ured; and under the same conditions should sustain a tensile 
strain of one hundred and seventy-eight pounds to the square 
inch of cross-section. 

Test for other varieties. — The relative value of other 
varieties of cements can be determined by subjecting them 
to similar tests and comparing the results. 

Wire Test. — The wire test was formerly used to determine 
the hydraulic activity of samples. It is as follows: The* paste 
is made into cakes of one and a quarter inches in diameter 
ami five : eighths of an inch thick, and is immersed in water of 
an established temperature (65° F.); the times :uv then noted 
which are required before the cakes will support, without de- 



MORTAR. 57 

pression, the point of a wire one-twelfth of an inch in diameter 
loaded to weigh one-quarter of a pound, and of another wire 
one twenty-fourth of an inch in diameter weighing one 
pound. This test is still used to some extent, especially by 
the French. 

The wire test, when applied to cement pastes without sand, 
does not give a correct indication of the values of their hy- 
draulic properties. 

STORAGE OF LIMES AND CEMENTS. 

118. Hydraulic limes and cements deteriorate by exposure 
to the air. If liable to be kept on hand for several months, 
they should be stored in a tight building free from draughts 
of air, and the casks should be raised several inches above the 
floor, if stone or earthen. 

Cements, that have been injured by age or exposure, may 
have their original energy restored by recalculation. Samples 
have been restored by being submitted to a red heat of one 
hour's duration. 

Common lime, for the same reasons, should' be preserved in 
tight vessels. It is usually sent to market in barrels, and is re- 
duced to powder by slaking. The fineness of the powder, its 
growth, the phenomena of slaking, and the degree of unc- 
tuousness of the paste made with water, are the tests for good 
lime. 



MORTAR. 

119. Calcareous Mortar, ready for use, is a mixture, in a 
plastic condition, of lime, sand, and w r ater. It is used to bind 
together the solid materials in masonry constructions, and to 
form coatings for the exterior surfaces of the walls and inte- 
rior of buildings. 

It may be divided into two principal classes — common 
mortar wdien made of common lime, and hydraulic mortar 
when hydraulic lime or cement is used. 

When mortar is thin-tempered or in a fluid state x it is 
known as grout. 

Hardened Mortar is simply an artificial stone, and should 
fulfil the essential conditions already given for stone — viz., 
should possess strength, hardness, and durability. These 
qualities ar£-dependent~en the quality of the lime or cement 
employed, the kind and quantity of sand, the method and 



58 CIVIL ENGINEERING. 

degree of manipulation, and the position, with respect to 
moisture or dryness, in which the mortar is subsequently 
placed. 

Common mortar will harden only partially in damp places 
excluded from free circulation of air, and not at all under 
water. These places are, on the contrary, favorable to the in- 
duration of hvdraulic mortars. 



SLAKING LIME. 

120. Before the lime is mixed with sand to form mortar, it 
must first be slaked. 

The methods of slaking lime are classed under three heads : 
1, drowning ; 2, immersion; and 3, spontaneous or air slak- 



The first is to throw on the lumps of lime, just as they 
come from the kiln, enough water to reduce them to paste. 
The workmen are apt to throw on more water than is required; 
hence the name. 

The second is to break the lumps of lime into pieces not 
exceeding an inch through, then to place them in a basket or 
other contrivance, and to immerse them in water for a few 
seconds, withdrawing them before the commencement of ebul- 
lition. A modification of this method is to form heaps of the 
proper size of these broken lumps, and then to sprinkle a cer- 
tain quantity of water upon the lime, the amount of water 
being from one-fourth to one-third the volume of the lime, the 
rose of a watering-pot being used in sprinkling. 

The third is to allow the lime to slake spontaneously by 
absorbing moisture from the surrounding atmosphere. 

The first method is the one most generally used in the 
United States. 

The lumps of lime are collected together in a layer from 
six to eight inches deep, in a water-tight box, or a basin of 
sand coated over with lime-paste to make it hold water, and 
then the amount of water sufficient to reduce the lime to a 
paste is poured over them. This amount of water is approxi- 
mately determined by a trial of a small quantity of lime be- 
forehand. It is important that all the water necessary should 
be added at the beginning. After an interval of five or ten min- 
utes the water becomes heated to the boiling-point, and all 
the phenomena of slaking follow. 

The workmen are apt to use too much water in the begin- 
ning, or, not using enough, to add more when the slaking is 



MORTAR. 59 

in progress. In the first case the resulting paste will be too 
thin, and in the latter the checking of the slaking will make 
the product lumpy. 

As soon as the water is poured on the lime, it is recommend- 
ed to cover the mass with canvas or boards, or with a layer of 
sand of uniform thickness after the slaking is well underway. 
Another recommendation is, that the lime be not stirred while 
slaking. 

Writers disagree as to the relative values of these three meth- 
ods of slaking lime. Supposing that in the first process all 
the water required to produce a stiff paste, and no more than 
this, is poured on at the beginning, these modes may be ar- 
ranged in their order of superiority, as follows : 

For fat limes : 1, drowning, or the ordinary method ; 2, 
spontaneous slaking ; and, 3, immersion. For hydraulic limes : 
1, ordinary method; 2, immersion; and, 3, spontaneous 
slaking. 

In the matter of cost, the first mode has a decided advan- 
tage over the others. The second is not only expensive from 
the labor required, but difficult from the uncertainty of the 
period of immersion at the hands of the workmen. The 
third involves the expense of storage-rooms or sheds and time, 
a period from twenty days to even a year being necessary to 
complete the slaking. 



PRESERVATION OF THE LIME AFTER BELXG SLAKED. 

121. The paste obtained by the first mode may be pre- 
served any length of time if kept from contact with the 
air. It is usual to put it in tight casks, or in reservoirs ; 
in trenches and covered with sand will be sufficient for its 
preservation. 

The powder, from the second and third modes, may be pre- 
served for some time, by placing it in casks or bins with cov- 
ers, or in dry sheds in heaps, covered over with cloth or dry 
sand. 

General Treussart thought that lime should be used imme- 
diately after it was slaked. In this country such is the ordi- 
nary practice. The general opinion of engineers is however 
adverse to this practice, and in some parts of Europe it is 
the custom to slake the lime the season before it is used. 



60 CIVIL ENGINEERING. 



SAND. 

122. Sand is the granular product arising from the disinte- 
gration of rocks. It may therefore, like the rocks from which 
it is derived, be divided into three principal varieties — the 
silicious, the calcareous, and the argillaceous. 

Sand is sometimes named from the locality where it is ob- 
tained, as pit-sand, which is procured from excavations in in- 
land deposits of disintegrated rock ; sea-sand and river-sand, 
which are taken from the shores of the sea or rivers. 

Builders again classify sand according to the size of the 
grain. The term coarse sand is applied when the grain va- 
ries between |- and T ^ of an inch in diameter ; the term fine 
sand, when the grain is between ^ and -Jt of an inch in di- 
ameter ; and the term mixed sand is used for any mixture 
of the two preceding kinds. 

The usual mode of determining the size of sand is to screen 
it by passing it through sieves of various degrees of fineness. 
The sieves are numbered according to the number of open- 
ings in a square inch of the wire gauze of which they are 
made. 

The silicious sands, arising from the quartzose rocks, are the 
most abundant, and are usually preferred by builders. The 
calcareous sands, from hard calcareous rocks, are more rare, 
but form a good ingredient for mortar. Some of the argilla- 
ceous sands are valuable, as when mixed with common lime 
they impart to it hydraulic properties. 

The property, which some argillaceous sands possess, of 
forming with common or slightly hydraulic lime a compound 
which will harden under water, has long been known in France, 
where these sands are termed arenes. The sands of this na- 
ture are usually found in hillocks along river valleys. These 
hillocks sometimes rest on calcareous rocks or argillaceous 
tufas, and are frequently formed of alternate beds of sand 
and pebbles. The sand is of various colors, such as yellow, 
red, and green, and seems to have been formed from the dis- 
integration of clay in a more or less indurated state. They 
form, with common lime, an excellent mortar for masonry, 
exposed either to the open air or humid localities, as the foun- 
dations of edifices. 

Pit-sand has a rougher and more angular grain than river 
or sea sand, and on this account is generally preferred by 
builders for mortar to be used in brick or stone work. 

River and sea sand are by some preferred for plastering, 



MORTAR. CI 

because they are whiter and have a finer and more uniform 
grain than pit-sand. 

The sand used in common mortar should be clean, sharp, 
and neither too coarse nor too fine. 

Its cleanliness may be known by its not soiling the fingers 
when rubbed between them ; and its sharpness can be told by 
filling the hand and closing it firmly, listening to the sounds 
made by the particles when rubbed against each other. 

Dirty sand, as well as sea sand, should before using be 
washed, to free it from impurities. 

Sand enters mortar as a mechanical mixture, and is»used to 
save expense by lessening the quantity of lime, to increase 
the resistance of the mortar to crushing, and to lessen the 
amount of shrinking during the drying of the mortar. 
. It injures the tenacity of mortar, and if too much be used 
the mortar will crumble to powder when it dries 



PROPORTIONS OF INGREDIENTS. 

123. The quantity or proportion of sand to the lime varies 
with the quality of the lime and the uses to be made of the 
mortar. 

Yicat gives for common mortar the proportion of 2.4 parts 
of sand to one of pure slaked lime in paste, by measure. 

The practice of the United States Corps of Engineers in 
making hydraulic mortars has been to add from 2.5 to 3.5 in 
bulk of compact sand to one of lime and cement, or cement 
alone, in thick paste. 



THE METHOD AND DEGREE OF MANIPULATION. 

124. The ingredients of mortar are incorporated either by 
manual labor or by machinery; the latter method gives re- 
sults superior to the former. The machines used for mixing 
mortar are the ordinary pug-mill (Fig. 7), like those employed 
by brickmakers for tempering clay, the grin ding-mi 11 (Fig. 8), 
or mill of any other pattern suitable for the work. The grind- 
ing-mill is a better machine for this purpose than the pug-mill, 
because it not only reduces the lumps found in the most care- 
I fully-burnt stone after the slaking is apparently complete, but 
it brings the lime to the state of a uniform stiff paste, in 
which condition it should be before the sand is incorporated 
with it. 



62 



CIVIL ENGINEERING. 




Fig. 7 represents a vertical 
section through the axis of a pug- 
mill for mixing or tempering 
mortar. This mill consists of a 
hooped vessel of the form of a 
conical frustum, which receives 
the ingredients, and of a vertical 
shaft, to which arms with teeth 
resembling an ordinary rake,- are 
attached for the purpose of mix- 
ing the ingredients. 

A, A, section of sides of the 
vessel. 

B, vertical shaft, to which the 
arms C are affixed. 

D, horizontal bar for giving a 
FlG - 7 * circular motion to the shaft B. 

E, sills of timber supporting the mill. 

F, wrought-iron support, through which the upper part of 
the shaft passes. 

Fig. 8 represents a part of a mortar mill for crushing 
lime and tempering mortar. 

A, a heavy wheel of timber or 
cast iron. 

B, a horizontal bar passing 
through the wheel, fixed to a 
vertical shaft, and arranged at 
the other end, C, with the 
proper gearing for a horse. 

D, a circular trough which 
receives the ingredients to be 
mixed. The trough is of trape- 
zoidal cross-section, from 20 to 
30 feet in diameter, about 18 inches wide at top, 12 inches 
deep, and is built of hard brick, stone, or timber laid on a firm 
foundation. 

A good example of a grinding-mill is given on page 98 of 
Lieut. W. 11. Wright's " Treatise on Mortars," in describing 
the mill used at Fort Warren, Boston Harbor. 

The steam mortar-mill, in which the wheels or stones 
revolved on edge, and which was used at Fort Taylor, Key 
West, Florida, the mortar mill of Greyveldinger, used in 
Paris, in which a revolving screw performs the mixing, as 
also the Fort Warren mortar-mill above alluded to, are de- 




Fm. 8. 



MORTAR. 63 

scribed in Gillmore's "Treatise on Limes, Cements, and 
Mortars." 

125. Process of making Mortar with the Mill. — The 

lime-paste is first put in the circular trough, and to this is 
added by measurement about one-half of the sand required 
for the batch. The mill is set in motion, and the ingredi- 
ents thoroughly incorporated. The remainder of the sand is 
then added, and as much water as may be necessary to bring 
the mass to the proper consistency. 

If common mortar is to be rendered hydraulic by adding 
hydraulic cement, the latter should be added to the lime-paste 
just before the mill is set in motion ; a very quick-setting 
cement should not be added until the last portions of sand are 
thrown in. 

126. Process by Hand. — The measure of sand required 
for the batch is placed on the floor and formed into a basin. 
in which the unslaked lime is placed, the lumps being broken 
to the proper size. The necessary quantity of water is poured 
on by a hose, watering-pots, or ordinary buckets, and the lime 
stirred as long as vapor is evolved. The ingredients are well 
mixed together with the shovel and hoe, a little water being 
added occasionally if the mass be too stiff. It is customary 
then to heap the mortar compactly together, and allow it to 
remain until ready for use. 

The rule in mixing mortar, either by machinery or hand, 
is to see that the lime and sand he thoroughly incorporated. 



SETTING- OF MORTARS. 

127. A mortar has set when it has become so hard that its 
form cannot be altered without fracture. The set is deter- 
mined by the wire test. If the mortar supports the point of 
the wire without depression or penetration, it is assumed that 
the mortar has set. 

THEORY OF SETTING- OF MORTARS. 

128. Common mortar slowly hardens in the air, from the 
surface towards the interior, by drying and by the absorption 
of carbonic acid. The process is slow, but in time, under 
favorable circumstances, a hard material is produced. The 
carbonic acid, absorbed by the mortar, combines with the 
lime, forming a carbonate with an excess of base, and the 
hardening is due to this reaction and to pressure. 



64: CIVIL ENGINEERING. 

Hydraulic mortars, and paste made with hydraulic cement, 
harden by a species of crystallization that takes place when 
the silicates of lime, alumina and magnesia, which are anhy- 
drous after calcination, become hydrates upon being mixed 
with water. 

The compounds which are formed by burning the lime- 
stone fit to produce Portland cement at a high heat require 
but three equivalents of water for their hydration, while those 
formed at a low heat take six. This is probably the cause of 
the superior strength and hardness attained by the Portland 
cement. 

In the cements obtained from the argillo-magnesian lime- 
stones the presence of the silicate of magnesia is given as the 
reason why these cements are more durable for constructions 
in the sea, as the silicate of magnesia resists the action of sea- 
water better than the silicates of lime and alumina, unless 
other ingredients introduce adverse conditions. 

ADHERENCE OF MORTAR. 

129. The force with which mortars, in general, adhere to 
other materials depends on the nature of the material, its 
texture, and the state of the surface to which the mortar is 
applied. 

In applying mortars, the materials to be joined should be 
thoroughly moistened — a point too often neglected — and 
the surfaces made clean. Precautions should be taken to 
prevent too rapid drying, and the mortar should be as stiff as 
it can be used, still being in a plastic condition. 

Mortar adheres most strongly to brick, and more feebly to 
wood, than to any other material. Among stones of the same 
class it generally adheres better to the porous and coarse- 
grained than to the compact and fine-grained. Among sur- 
faces it adheres more strongly to the rough than to the 
smooth. 

The adhesion of common mortar to brick and stone, for the 
first few years, is greater than the cohesion of its own par- 
ticles. The contrary is the case with hydraulic cement. 

From experiments made by Rondelet on the adhesion of 
common mortar to stone, it appears that it required a force 
varying from 15 to 30 pounds to the square inch, applied 
perpendicular to the plane of the joint, to separate the mortar 
and stone after six months' union ; whereas only 5 pounds to 
the square inch were required to separate the same surfaces 
when applied parallel to the plane of the joint. 



MORTAR. 65 



130. The same general rules for determining these qualities 
in stone are applicable in mortars, and, as with stone, experi- 
ence is the best test. 

The principal causes of deterioration and decomposition of 
mortars are : 

1. Changes of temperature, producing expansions and con- 
tractions. 

2. Alternations of freezing and thawing, producing ex- 
foliations and disintegrations of the parts exposed to their 
influence. 

Common mortars, which have had time to harden, resist 
the action of severe frosts very well, if they are made rather 
poor, or with an excess of sand. The proportions should 
be 2-J- volumes, or over, of sand to one of the lime in paste. 

Hydraulic mortars set equally well in damp situations and 
in the open air ; and those which have hardened in the air 
will retain their hardness if afterwards immersed in water. 
They also resist well the action of frost, if they have had time 
to set before exposure to it ; but, like common mortars, they 
require to be made with an excess of sand to withstand well 
atmospheric changes. 

To ascertain the strength and compare the qualities of 
different mortars, experiments have been made upon the 
resistance offered by them to cross-strains. 

The usual method has been to place small rectangular 
prisms of mortar, upon points of support at their extremities, 
and subject them to a cross-strain by applying a pressure at 
a point midway between the bearings. 

131. Experiments made upon prisms a year old, which had 
been exposed to the ordinary changes of weather, gave the 
following as the average resistances per square inch offered 
by mortars to a force of traction ; the deductions being drawn 
'rom. experiments on the resistance to a transverse strain : 

Mortars of very strong hydraulic lime .... 170 pmmds. 
" ordinary " " < < .... 140 " 

" medium " " .... 100 " 

' ( common lime 40 i( 

" (bad quality).... 10 << 

General Totten, late Chief of Engineers TJ. S. Army, from 
his experiments on mortars, deduced the following general 
results : 

5 



66 CIVIL ENGINEERING. 

1. That mortar, of hydraulic cement and sand, is the stronger 
and harder as the quantity of sand is less. 

2. That common mortar is the stronger and harder as the 
quantity of sand is less. 

3. That any addition of common lime to a mortar of 
hydraulic cement and sand, weakens the mortar, but that a 
little lime may be added without any considerable diminution 
of the strength of the mortar, and with a saving of expense. 

4. The strength of common mortars is considerably im- 
proved by the addition of an artificial pozzuolana, but more 
so by the addition of an hydraulic cement. 

5. Fine sand generally gives a stronger mortar than coarse 
sand. 

6. Lime slaked by sprinkling gave better results than lime 
slaked by drowning. A few experiments made on air- 
slaked lime were unfavorable to that mode of slaking. 

7. Both hydraulic and common mortar yielded better re- 
sults when made with a small quantity of water than when 
made thin. 

8. Mortar made in the mortar-mill was found to be superior 
to that mixed in the usual way with a hoe. 

9. Fresh water gave better results than salt water. 



USES OF MORTAR FOR STUCCO, PLASTERING, ETC. 

132. The term plastering is ordinarily limited to the cover- 
ing of interior walls and ceilings by coats of mortar, while 
the mortar covering exterior walls is called stucco. This 
latter term was originally applied to a species of plastering 
made to resemble marble, being quite hard and capable or 
receiving a polish. Outside plastering is used often to pre- 
vent the rain from penetrating the joints of the masonry, and 
in general when it is desired to have a smooth surface instead 
of a rough one. 

Both inside and outside plastering, when properly done, 
require three coats to be used, the first known as the scratch 
coat, the second as the brown, and the third as hard finish, 
or stucco. The first coat is common-lime mortar, with a given 
quantity of bullock's hair mixed with it. It contains" ordi- 
narily a larger proportion of sand than common mortar does, so 
as to reduce the shrinkage to a minimum. When completed , 
and partially dry, and still soft, it is with a pointed stick 
scratched in parallel scorings running diagonally across the 
surface at right angles to each other. When the first coat is 



MASTIC. 67 

dry enough, the brown coat is applied. This differs from the 
first in containing less hair in the mixture. This is followed 
by the third coat, which is hard finish for the inside, or 
stucco for the outside. The former is a paste of fine lime 
and plaster of Paris ; the ktter is a paste of fine lime made 
stiff with white sand. 

If the outer plastering is to be exposed to the weather, it 
should be made of hydraulic mortar. 

3d. — MASTICS. 

133. Mastic is the term generally applied to a mixture of 
artificial or natural combinations of bituminous or resinous 
substances with ot h er iiig i rtifchT s. jw\-v* ^ ^ r , 

It is used as a cement for other ' materials, or as a coating %k~£Ta 
to render them water-proof. 

The term asphalt is sometimes employed to designate the 
bituminous limestone, more generally the mastic after it has 
been moulded into blocks for transportation, frequently to 
the product obtained by mixing sand with the mastic, and by 
some to the raw bitumen or mineral tar. Callicg the first 
asphalt, the second would be asphaltic mastic, the third 
asphaltic concrete, and the fourth asphaltum. 



BITUMINOUS MASTIC. 

134. Bituminous mastic is prepared by heating the min- 
eral pitch or asphaltum in a large caldron or iron pot, and 
stirring in the proper proportion of the powdered limestone. 
This operation, although very simple in its kind, requires 
great attention and skill on the part of the workmen in 
managing the fire, as the mastic may be injured by too low 
or too high a degree of heat. The best plan appears to be to 
apply a brisk fire until the boiling liquid commences to give 
out a thin, whitish vapor. The fire is then moderated and 
kept at a uniform state, and the powdered stone is gradually 
added, and mixed in with the tar by stirring the two well 
together. If the temperature should be raised too high, the 
heated mass gives out a yellowish or brownish vapor. In this 
state it should be stirred rapidly, and be removed at once 
from the fire. 

When' the mixing is completed, the liquid mass is run into 
moulds, where it hardens into blocks of convenient shape and 
size. 



68 CIVTL ENGINEERING. 

The stone above used is a carbonate of lime naturally im- 
pregnated with bitumen, called sometimes Seyssel asphalt, 
from the place where it was quarried. The proportion of 
bitumen in the Seyssel stone is oftentimes as much as 17 per 
cent., and the amalgamation is more perfect than that of any 
artificial compound of the kind yet invented. To prepare it 
for the operation just described, the stone may be reduced to 
powder, either by roasting it in vessels over a fire, or by grind- 
ing it down in the ordinary mortar-mill. To be roasted, the 
stone is first reduced to fragments the size of an egg. These 
fragments are put into an iron vessel, heat is applied, and the 
stone is reduced to powder by stirring it and breaking it up 
with an iron instrument. This process is not only less eco- 
nomical than grinding, but the material loses a portion of the 
bitumen from evaporation, besides being liable to injury from 
too great a degree of heat. If to be ground, the stone is first 
broken as for roasting. Care should be taken, during the 
process, to stir the mass frequently, otherwise it may cake. 

To use the mastic, the blocks are remelted, and the mixture, 
in this state or mixed with sand, is laid on the surface to be 
coated by pouring it on, generally in squares, care being taken 
to form a perfect union between edges, and to rub the sur- 
face smooth with an ordinary wooden float, especially if it is 
to receive another layer. 

135. Proportions. — The proportions for bituminous mastic 
are about 1 part of asphaltum to 7 or 8 by measure of the 
powdered limestone, according as the stone contains more or 
less bitumen. 

Aii} T petroleum or naphtha present in the stone must be 
removed ; this is generally done by distillation. Clay in the 
limestone injures the mastic, and is oftentimes the cause of 
the cracks seen in asphaltic concrete after it has been laid. 



ARTIFICIAL MASTICS. 

136. Artificial Mastics have been formed by mixing coal- 
tar, vegetable tar, pitch, etc., with powdered limestone, pow- 
dered brick, litharge, etc.; but these mixtures are inferior to 
the bituminous mastic. 

The impurities and volatile ingredients of coal-tar, mineral 
tar, and similar substances, render them less durable than 
mineral pitch, and the combinations made with them are in- 
ferior to those made with the latter, as might be expected. 
But, for certain purposes, the artificial mastics are extremely 



PRESERVATIVES. 69 

useful, as they are quite cheap and possess in a measure the 
advantages of bituminous mastic. 



USES OF MASTICS. 

137. The combinations of asphaltum were well known to 
the ancients, and a cement made of it is said to have been 
employed in the construction of the walls of Babylon. 

The principal uses of mastic at the present day are for 
paving streets, sidewalks, floors, cellars, etc., and for forming 
water-tight coatings for cisterns, cappings of arches, terraces, 
and other similar roofings. 

It has quite an extensive use in Europe at the present time. 
The principal sources of the asphalt are the Jurassic range in 
the Yal de Travers, Pyrimont, Seyssel on the Rhone, and the 
neighboring localities, and Bechelbronn (or Lobsan), in Alsace. 

Asphaltum alone has been frequently used for coatings, but 
in time it becomes dry and peels off. But made into mastic, 
evaporation is prevented and its durability increased. 

The use of the mastic, for making asphaltic concrete, has 
already been described. 



CHAPTER Y. 

PRESERVATIVES. 

PAINTS. 



138. Paints are mixtures of fixed and volatile oils, chiefly 
those of linseed and turpentine, with certain of the metallic 
salts and oxides, and with other substances ; the latter are used 
either as pigments or stainers, or to give what is termed a body- 
to the paint, and also to improve its drying properties. 

Paints are mainly used, as protective agents, to secure wood 
and metals from the destructive action of air and water. As 
they possess only a limited degree of durability, they must be 
renewed from time to time. They are more durable in air 
than in water. 

The principal materials used in painting are : Red and 



70 CIVIL ENGINEERING. 

white lead, red and yellow ochre, prussian blue, verdi- 
gris, lamp-black, litharge, linseed-oil, and spirits of tur- 
pentine. 

By suitably combining the above, almost any color may be 
obtained. For example, a lead color is obtained by mixing a 
little lamp-black with the white lead, etc. 

Linseed-oil, being boiled with the addition of a small quan- 
tity of litharge and sugar-of-lead, forms what is known as 
drying oil. 

Spirits of turpentine is not generally used in the paints 
intended for external and finishing coats, as it does not stand 
exposure as well as oil. 

139. In painting wood, the first thing to be done is to clean 
and smooth the surface' to be covered. If the wood be resin- 
ous the knots must be killed before the paint is applied ; this 
is done by applying a coat of red lead mixed with sizing. 
The surface being dry, the first coat, generally white lead 
mixed with linseed oil, is put on ; this is called priming. 
This coat being dry, all holes, indentations, heads of nails, 
etc., should be filled and covered over with putty. The 
second coat of paint is then applied. If it be old work that 
is to be repainted, the entire surface should be scrubbed with 
soap and water, well scraped, and then rubbed down with 
sand-paper or pumice, in order to get rid of the old paint 
and to obtain an even, smooth surface. 



JAPANNING. 

140. Japanning is the name given to the process which 
forms over the surface of the material to be covered, a hard, 
smooth, varnish-like coating. [Art. 80.] 



OILING. 

141. Oiling is frequently used as a preservative. It may 
be done either while the surface to be protected is hot or cold. 
Linseed-oil is the material generally used. 



VARNISHES. 

142. Varnishes are made by dissolving resinous substances 
in alcohol, or linseed-oil and spirits of turpentine, just as 
paints are made by similarly dissolving or mixing pigments. 



PRESERVATIVES. 71 

Varnishes are used for the same purposes as paints, when it 
is desired to give a clear, shining appearance to the surface 
on which they are laid. 



COAL-TAR. 

143. Goal-tar is much used as a preservative. It may be 
applied as a coating for the material, or it may be applied by 
the process known as " creosoting." [Art. 25.] 



ASPHALTUM. 

144. Asphaltum is used for the same purposes. Its uses 
are described in Art. 137. 



METAL COVERINGS. 

145. Plating. — Protection is frequently afforded by cover- 
ing the material with a thin coating of metal ; the latter not 
being affected, or to a very slight degree, by the destructive 
agencies to be guarded against. 

Zinc applied to iron, by the process of " galvanizing," pro- 
tects iron from direct action of the air and moisture as long 
as the coating is perfect. [Art. 82.] 

Tin is used for the same purpose. 

Nickel has been tried for brass. 



OTHER PRESERVATIVES BY CHEMICAL COMBINATIONS. 

146. Salts of Silica have .been tried for protection of 
building stones. [Art. 35.] 

Various salts have been used to saturate timber, thus* 
changing the albuminous substances in the timber into insol- 
uble compounds by chemical action, and thus increasing its 
durability. [Art. 25.] 






V 



72 CIVIL ENGINEERING. 



PART II. 

STRENGTH OF MATERIALS. 



CHAPTER VI. 

STRAINS- 

147. The materials in a structure are subjected to the 
action of various forces, according to the kind of construction 
of which they form a part, and the position they occupy in it. 

In planning a structure, two general problems are to be 
considered. 

I. The nature and magnitude of the forces which are to 
act on it ; and, 

II. The proper distribution and size of its various parts, so 
that they shall successfully resist the action of these forces. 

In the former, if the intensities, directions, and points of 
application be known, the effect that the forces will exert 
may be determined. 

In the latter, it is necessary to have a knowledge of the 
strength of the materials to be used in the structure. 

148. Strength depends upon the internal organization of 
a body, and a material is said to have the requisite strength — 
to be strong enough — when, by reason of certain inherent 
physical properties, it possesses the ability to resist the action 
of an external force within limits. 

All materials have not equal strength, nor does the same 
material resist equally the same force, when a change is 
made in its direction or point of application. 

The degree of strength that a material possesses is deter- 
mined by experience or experiment. 

As it is not always practicable nor expedient to submit to 
the test of an actual experiment the piece to be used in a 
structure, its assumed degree of strength is obtained cither 
by subjecting a piece of the same material, having the same 
dimensions, to conditions similar to those to which t\w for- 
mer is to be submitted; or knowing the relations between 



STRAINS. 73 

tlie strengths of pieces of the same material of different di- 
mensions, by deducing it. These relations are obtained from 
mathematical principles, and are confirmed by experience. 

In deducing them, every solid is supposed to be formed 
of molecules, which are infinitely small and infinitely close to 
each other, grouped together by certain laws. Each mole- 
cule is supposed to be so related to those surrounding it, 
that its position cannot be changed except by the application 
of an extraneous force. 

If any extraneous forces act at different points of a solid 
which is not allowed to move from its place, the equilibrium 
of the internal forces acting between the molecules will be 
disturbed. 

This disturbance will cause variations in the distances be- 
tween the molecules, and in the directions and intensities of 
the internal forces that bind them together. 

By these variations an equilibrium between the impressed 
and internal forces is effected, and an alteration of the form 
of the solid is caused. These alterations of form are called 
strains. 

149. The w T ord strain is applied indifferently to denote 
either the system of forces acting on the solid to alter its 
form, or to the alteration of form produced by it. 

The word stress is frequently used to denote the system 
of forces acting on the solid; limiting the "term strain to 
the alteration of form caused by them. 

Stress will be so used in this subject to denote the force 
or system of forces acting to produce a strain. 



CLASSIFICATION OF STEAINS. 

150. The different pieces of which a frame or structure is 
composed are ordinarily similar in shape to right prisms, and 
have generally a plane of symmetry in which are applied 
the extraneous forces whose actions they are intended to re- 
sist. These pieces may be considered as formed of an infi- 
nite number of fibres, each of which may be regarded as a 
right prism, having an infinitely small area for its base, and 
its edges parallel to those of the prism. 

If one of these pieces be intersected by an infinite number 
of planes, each perpendicular to its edges, these planes will 
divide the fibres into infinitely small solids, each of which 
may be considered as the element of a fibre ; and if these 
elementary solids, or fibres, be referred, in the usual manner, 



74 



CIVIL ENGINEERING. 



to three rectangular axes, two of which, as Z, and Y, are con- 
tained in a plane perpendicular to the edges of the prism, 
and the third, X, is parallel to them; then the area of the 
base of any elementary fibre will be expressed by dz x dy, 
and its length by dx. 

In considering the elementary fibres contained between 
any two of these consecutive planes, it will be seen that, 
although the relative positions of the planes may be varied in 
many ways, they admit of four simple relative movements, 
which, either singly or combined, will, in the elementary 
fibres between them, produce all the varieties of change of 
form arising from these changes of positions, and will illus- 
trate all the strains to which the piece may be exposed. 

For example, let (Fig. 9) represent the longitudinal sec- 
tion, and (Fig. 10) the cross-section of any piece, and A B, and 
C D, two of the consecutive planes in question. 



o o; 



ffrf-/ 



It- - 4 



A c 6 



^ 



BD'D 



,-W 




Fig. 9. 



Fig. 10. 



The four movements will be as follows : 

1st. The plane, C D, may be m ovod parallel to A B, .either 
from or towards it. In the former case, the elementary 
fibres between the planes will be lengthened, and, in the lat- 
ter, shortened ; and the strains to which they are subjected 
will arise from a force of extension in the first case, and of 
compression in the second, acting parallel to the fibres. 

2d. The plane, C D, may take the position, C' D', by turn- 
ing around some line, 0, in it as an axis, in which case the 
elementary fibres on one side of this axis, in conforming to 
the new position of C D, will be deflected and lpngthened, 
undergoing a strain of tension ; whilst those on the opposite 
side will be deflected and shortened, undergoing a strain of 
compression ; and those, as 0', in the plane of the axis of 
the prism and of the axis of rotation, will be simply de- 



flected, without any change in their original length ; the 
plane, C D, in its new position C D', continuing normal to ail 
the elementary fibres in their new position of deflection. 

The strains in this case will arise from a force acting trans- 



aszb 



STRAINS. 75 

versely to the piece, tending to bend it. This force produces 
transverse or cross strain. 

3d. The plane, C D (Fig. 11), may receive a motion of 

translation in the direction C D, parallel i a c 

to A B, in which any elementary fibre, 
as a 5, will take a new position, as a b', 
oblique to its original position. 

The strains in this case will arise from ~~ b d 

a force acting transversely, tending to Fig. U. 

force one part of the solid over an adjacent part, similar to 
the action seen in a pair of shears. This force produces a 
transverse shearing strain. 

4th. Or the plane C D may receive a motion of rotation 
around some axis perpendicular to it, in which case the base 
b of any elementary fibre, as a b, in the plane C D (Fig. 11), 
will take a new position, describing around the axis of rota- 
tion a small arc in the plane C D. 

The strains in this case will arise from a force of torsion. 

The resulting strains upon an elementary fibre, arising f rom- 
the simultaneous action of two or more of these forces, may 
be explained by combining two or more of the movements 
of the consecutive planes, as just described. 

These changes of positions of the planes are due to ex- 
traneous forces w T hose action is resisted by the molecular 
forces brought into play by the strains on the fibres of the 
piece. 

These actions and reactions give rise to several problems 
which, aided by experiment, may be solved by mathematics, 
and whose application is found in deducing the resistances 
offered by the solid parts of structures to the forces to which 
they are subjected. 

151. Weights, either permanently or temporarily applied, 
are the forces which ordinarily act upon the different parts 
of structures. The strains, caused by them, to which build- 
ing materials may be exposed, are : — 

I. Compression ; as in the case of a weight, resting on the 
top of a pillar or post, tending to compress the fibres. 

II. Tension ; as in the case of a weight, suspended from 
one end of a rod, rope, chain, etc., the other end being fixed, 
tending to stretch or lengthen the fibres. 

III. Transverse or Cross Strain ; as in the case of the 
load on the timbers of floors and on beams generally, tending 
to bend them. 

IV. Shearing Strain; as in the case of rivets of iron 
plates, pins in bridges, etc., where equal forces are applied 



76 CIVIL ENGINEERING. 



< jui^ / 1 



on opposite sides in such a manner as to tend to force one 
part over the adjacent one. 

V. Torsion ; a twisting fo^^e of rare occurrence in build- 
ing, but common in machinery. 

152. The effect of thegg straining forces is : 

1st. Within certain limits to produce only an alteration of 
form, and 

2d. If sufficiently great, to produce rupture or separa- 
tion of the parts. 

The resistances offered to these am due to the properties of 
elasticity and cohesion in the solid. 

Elasticity is the property by which a body offers a resist- 
ance to change of figure, and tends to resume its form when 
the extraneous force producing the strain is removed. If the 
recovery of form is perfect, the body is said to be perfectly 
elastic. 

Cohesion is the property which binds the particles together 
into one mass, and opposes their separation by any extraneous 
force. 

Many experiments have been made, both in this and foreign 
countries, to determine the limits of these properties for the 
ordinary building materials. 

The knowledge of the capacity of the different parts of a 
structure to sustain the permanent and temporary loads which 
it may have to bear, is essential to the engineer, and the object 
of the division, known as " Strength " or "Resistance of 
Materials," is to obtain this information. 



constants. 

153. In the solution of the problems that follow, and in 
their applications to determining the strength of building 
materials, certain constants are involved which depend for 
their value on the physical properties of the material under 
consideration. 

There are four principal ones : 

I. The weight, or specific gravity of the body ; 

II. The limit of elasticity; 

III. The coefficient of elasticity , 

IV. The modulus of rupture. 

These constants have boon or are to be determined for each 
material by actual experiment. 



CONSTANTS. 77 



The Weight. 

154. This must be known, as it enters as an element in all 
constructions ; and to such an extent in some, as in masonry 
structures, for example, that the moving or temporary loads to 
be borne by them may in comparison with it be disregarded. 



Limit of Elasticity. 

155. Different materials possess the property of elasticity 
in different degrees. In some the elasticity is very great, in 
others very little. 

If the applied forces producing a strain in a body be 
removed, and the body does not regain its former shape, 
there will be a permanent alteration in form, termed a set. 
To have produced this, the strain must have passed beyond 
the limit of elasticity. 

The limit of elasticity may be defined to be the greatest 
limit of the s train to which a material may be subjected, 
without producing a set. 

It is claimed that there will always be a set whenever an 
extraneous force, however small, is applied. Sets of this 
kind are microscopically small, and no practical error is made 
in assuming that they do not exist, that the material resumes 
its original shape. 

From a great number of experiments, made on a great 
variety of materials, it has been found that practically, 

1st. All bodies are elastic. 

2d. Within very small limits they may be considered as 
perfectly elastic. 

3d. Within the elastic limit the amount of displacement is 
directly proportional to the force that produces it. 

4th. Within a considerable distance beyond the elastic limit 
the amount of displacement is not exactly but nearly propor- 
tional to the force producing it. 

To determine experimentally the limit of elasticity of a given 
material for a strain of tension — as, for example, a rod or bar 
having one extremity fixed and the other acted on by a force 
to lengthen it, as by a weight suspended from one end — it 
would be necessary to note the different changes in the 
length of the bar made by successive applications and 
removals of weights, increasing them gradually and contin- 
ually until one is obtained which produces a set. The one 



78 CIYTL ENGINEERING. 

used just before this would express the limit for that particu- 
lar bar. 

Its value thus obtained would depend upon the care taken 
in making the experiment and upon the accuracy of the 
measurements. 

This limit seems to be affected by the length of time allowed 
in making the experiment; the limit being less when the 
weights are allowed to remain for a long time than when 
they remain only for short periods. 

The strains to which each piece in the structure is subjected 
must be within the limit of elasticity, or a permanent altera- 
tion of form results. 

Experience and experiment have fixed a certain limit 
allowable in practice for each kind of material. This limit 
of practice may by some sudden or unforeseen cause be 
passed ; but provided the limit of elasticity be not passed, 
no bad results will follow. This difference between the limit 
of elasticity and that of practice may be regarded as the 
measure of safety of the structure. 

The determination of the limit of elasticity is a matter of 
great nicety ; hence experimenters have paid more attention 
to determining, the ultimate strength of materials, that is, 
finding the limits beyond which any additional load will 
break the material. 



Coefficient of Elasticity. 

156. If a bar, of homogeneous material and prismatic form, 
is fixed at one end, and is acted upon by an external force, 
whose direction coincides with the axis of the bar, the bar 
will be either elongated or compressed, depending upon 
whether the force acts from or towards the fixed end. 

Represent by 
W, the force acting on the bar, 
L, the length of the bar, 
A, the area of its cross section, 

Z, the corresponding elongation -or contraction of the bar 
produced by the force, W. 

W 

Then — will be the force acting on the unit of cross section. 

Within the limits of elasticity, the elongation or contrac- 
tion of the bar varies directly with the force applied. 

Assume this law to be true for all values of the changes 



/M 



'in length of the bar produced by forces acting as just 

W 

stated. Then, since -^- is equal to the force on the unit of 

cross section producing an elongation equal to £, it is evident 
that the force necessary to produce an elongation equal to L 

must be -^- as great, or — — x — s- will be the force acting on 

the unit of cross section necessary to produce an elongation of 
the bar equal to L. a 

Denoting this force by E, we have 

-14 « 

This force is called the coefficient of elasticity. Some- 
times the term modulus of elasticity is applied to it. 

It is a theoretical force ; but as the law upon which it de- 
pends is practically true within the limits of elasticity, know- 
ing W", A, and L, and determining I by measurement, the 
value that E would have, if the law were true, can be found. 

Its value is constant for the same material, and depends upon 
the nature of the material. Experiments have been made, and 
the following are some of the values of the coefficients of 
elasticity for various materials : — 



Material. Value of E. 

Cast Iron 18,400,000 lbs. 

Wrought Iron 24,000,000 " 

Lead (cast) 720,000 " 

Steel 29,000,000 " 

Tin (cast) 4,608,000 " 

Zine (cast) 13,680,000 " 

Ash, , 1,644,800 " 

Fir 2,191,200 " 

Pine, pitch 1,225,600 " 

" yellow 1,600,000 " 

Oak 1,451,200 " 

Marble 2,520,000 " 

Limestone (common) 1,533,000 " 



Modulus of Rupture. 

157. If the forces applied to a body be continually increased, 
they at length produce rupture, or such a disfigurement as 
to render the body useless. 



80 CIVIL ENGINEERING-. 

Many experiments have been made on almost every kind 
of building material to determine this constant for each class 
and each particular kind. 

In the case of the experiment with the bar strained by a 
weight suspended from one extremity, if these weights be 
increased gradually and indefinitely, the elongation would 
become more apparent and finally separation of the particles 
would take place. The last weight put on, would be the 
amount necessary to rupture the bar, and since it is 
supposed to have acted over the whole cross section uni- 
formly, the resulting weight or force divided by the area of 
cross-section would give the force necessary to pull asunder 
a bar of this material whose cross-section was unity. This 
force necessary to pull asunder a bar whose cross-section is 
unitv is called the modulus of strength or tenacity, and 
expresses the tenacity of the material. 

If the force had acted in the opposite direction the fibres 
would have been compressed and the rupture would have 
taken place by crushing. The force, divided by the cross- 
section, would give the force necessary to crush a bar whose 
cross-section was unity, and would express the resistance to 
compression for that material. 

It the forces had acted perpendicularly to the axis, as 
would be the case if the bar had been placed in a horizontal 
position, with one end firmly fastened and the other sustain- 
ing a weight, then the rupture of the bar would have in- 
volved both the tearing asunder and crushing of the fibres. 

When rupture ensues, caused by a force acting transversely 
to break the bar, the stress on the unit of surface at the point 
where the fibres first begin to tear apart, or to crush, measures 
the resistance of the material, and is called the modulus of 
rupture. 

This stress is usually designated by R, while that produced 
by tension is represented by T, and compression by C. 

It would seem that the respective values of R, C, and T for 
the same material would be the same, or at least nearly equal, 
and that one symbol might be used to represent the respec- 
tive values of the three. Experiment shows, however, that 
they are not equal, but vary considerably. 

The discrepancies observed are attributed to several causes, 
the principal one of which seems to depend upon the law 
of elasticity of the body on which the experiments were made. 

With certain kinds of materials, like brick, stone, etc., it is 
much easier to determine the force required to rupture them, 
than to determine their limit of elasticity. Therefore, for 



TENSION. 



SI 



these classes of materials, instead of making the limit of prac- 
tice depend directly upon the limit of elasticity, it is usual to 
have it bear a certain relation to the force that breaks or 
crashes them. 



TENSION. 

158. Relations between elongations and the forces 
producing them, the weight of the bar not being con- 
sidered. 

Having a bar of a given uniform cross-section, to deter- 
mine the elongation produced by a force acting in the direc- 
tion of its axis. 

Represent (Fig. 12) by 
L, the original length of the bar, 
W, the force applied to lengthen it, 
I, the elongation due to W, 
A, the area of the cross-section, 
E, the coefficient of elasticity. 

Then from eq. (1), we have 

WL 




l =H ■ ■ < 2 > 



which is the required formula. 

Also, 

W = EA \ 



(3) 



w 



If, in eq. (3), we make A = 1 and 
I =Lj we shall have 



W = E. 



(±) 



Fig. 12. 



That is, the coefficient of elasticity, E, is the force which, 
applied to a bar, the cross-section of which is a superficial 
unit, would produce an elongation equal to the original 
length of the bar, supposing its elasticity perfect up to this 
limit. 

Eq. (2) shows that the elongation from any force acting in 
the direction of the axis of the bar, is directly proportional 
to the length of the bar, and to the force itself, and inversely 
to the area of the cross-section, and coefficient of elasticity ; 
which is fully confirmed by experiment. 

6 



82 CIVIL ENGINEERING. 

Divide W by A, and we have 

— = the strain on a unit of cross-section. 
A 

If W be the force necessary to produce rupture when act- 
ing in the direction of the axis, then 

W 

— — s= T, the modulus of tenacity. . . . (5) 

Wood and iron are the two building materials most fre- 
quently exposed to this strain. The cohesive power of wood is 
greatest in the direction of the fibres, and in the tables showing 
the results of the experiments made on the strength of mate- 
rials, the tensile strength there given is taken with reference 
to that direction, unless otherwise stated. 

From eq.- (5), we have W = TA, from which knowing 
T and A, the force necessary to rupture the bar may be 
deduced. 

159. The following table gives the tensile strength, per 
square inch, as obtained by experiment upon some of the ma- 
terials frequently used in building : 

Material. Tensile Strength per sq. inch. 

Ash 10,8.03 lbs. to 24,033 lbs. 

Chestnut 11,891 " •'< 13,066 " 

Cedar " " 10,300 « 

Hickory 12,866 " " 40,067 " 

Oak, white 12,300 " "25,222 " 

" live 15,800 " 

Pine 11,400 " "19,200 " 

Fir 12,867 " " 16,833 " 

Hemlock 16,533 " 

Cast iron, common pig 15,000 " 

" " good common .... 

iron 20,000 " 

Bar iron 57,000 " 

" " Swedish 72,000 " 

Copper wire 60,000 " 

Steel, cast 128,000 " 

" shear 124,000 " 

" puddled 105,000 " 

Tin, cast 4,800 " 

Lead, " 1,S00 " 

Zinc 7,500 " 



TENSION. 83 

The specimens of wood in the foregoing list were dry and 
seasoned. The time of seasoning varying from one to fifteen 
years. They were grown in different parts of the United 
States, extending from the extreme north to the farthest south, 
and from the Atlantic coast to the Pacific. The differences 
in the localities from whence they were brought and the times 
of seasoning, explain the differences observed in the tensile 
strength of specimens of the same wood. . 

The tensile strength of the metals is materially modified by 
the processes of manufacture and by the impurities they 
contain. 

It is evident, from this table, and from what has been just 
stated, that it is not practicable to assume a value for the 
modulus of tenacity which will be safe and economical for a 
given material. Its value in any particular case should be 
determined by experiment; or before its value can be 
assumed, the quality of the material must in some way be 
known. 



The work expended in the elongation of the bar. 

160. The general formula from Anal. Mechanics is 
Q =fFds, 

in which P is the resistance, s the path of the point of appli- 
cation, and Q the quantity of work. 

In this formula, substitute W for P, and I the elongation 
for s, and we have 

Q =fwdl 
Substituting for W its value from eq. (3), there obtains, 



9=/ 



= / EAfA 



to represent the quantity of work. 

Integrating between the limits 1 = and I = V, we have, 



84 CIVIL ENGINEERING. 

From eq. (3) we have 



TV' being the particular value of TV producing the elonga- 
tion, V. 

Substituting this value of TV' in the preceding equation, 
and we have 



Q = iW'Z' (6) 



If, in the eq. 



Q = fwdl, 
TV were constant and equal to TV', then 

q = wfai, 

which integrated between the limits 1=0 and l—V will give 

Q = WT. 

This value of Q is twice that of Q in eq. (6) ; whence it 
follows that the work expended in producing the elongation. 
Z', by applying the force, TV 7 , at once, or having it constant, 
would be twice the work expended, if the force is applied by 
increments, increasing gradually from zero to TV'. 

Combining eqs. 

W = 1 ^L and Q = J TV'Z', 

Xj 

and eliminating l f , we get 

TV 2 L 



Q = i 



E A> 



whence it is seen that the work expended upon the elongation 
of the bar varies directly with the square of the force pro- 
ducing it, with the length of the bar, and inversely with the 
area of cross section and coefficient of elasticity. 



TENSION. 



85 




Elongation of a bar, its weight considered. 

161. To determine the elongation of 
a bar, under the same circumstances 
as the preceding case, when its weight 
is taken into consideration. 

In eq. (2), the weight of the bar 
being very small compared with W, it 
was neglected. 

To determine the elongation, con- 
sidering the weight of the bar, repre- 
sent (Fig. 13) by L, W, I, and A, the 
same quantities as before, by x, the 
original length of any portion as A C, 
by dx, the length of an elementary 
portion as CD, and by w, the weight 
of a unit of volume of the bar. the 
volume of the portion B C, will be ex- 
pressed by (L — x) A ; and its weight 
by (L — x) Aw. 

The total force acting to elongate the elementary portion 
C D, will be expressed by 



L47b 



Fig. 13. 



W + (L — x) Aw. 
Substituting this for "W", and dx for L in eq. ( }), we have 

W+(L — x) Aw 



elongation of dx 



EA 



dx. 



The total length of dx after elongation will, therefore, be 

W+(L — x)Aw 7 
ax -\ ^j — '- dx. 

Integrating this between the limits x — and x = L, there 
obtains, 



L + Z - L+ EA + ^A~ • • 

for the total length of the bar after elongation. 
This may be written, 

l + ; = .l(i + ^±J^- l ). 



(?) 



8Q CIVIL ENGINEERING. 

If, in this expression, we make W = 0, we have 



7 %wAL T 
l -~EA L ' 

In this, wAJj is the weight of the bar; representing this 
weight by W and substituting in last expressson, we have 

"~ EA' 

or the elongation due to the weight of the bar, is one half of 
what it would be if a weight equal to that of the bar were 
concentrated at the lower end. 

An examination of the expression, W + (L — x) Aw, shows 
that the strain on the different cross-sections varies with x, 
decreases as x increases, and is greatest for x == 0, or on the 
section at the top. Since the bar has a uniform cross-section, 
the strain on the unit of area is different in each section. 



Bar of uniform strength to resist elongation, 

162. To determine the form aJ>ar should have and he 
equally strong throughout, to resist elongation produced by a 
force acting in the direction of the a,xis of the bar, the weight 
of the bar being considered. 

Suppose the bar, fixed at one end and the applied force 
producing elongation to be a weight suspended from the 
other end. [Fig. 14.] 

From the preceding article, it is seen that if the bar has a 
uniform cross-section, that the strain, on each section is dif- 
ferent. In order that the bar should be equally strong 
throughout, the strain on each unit of area of cross-section 
must be the same throughout the bar. This can only be 
effected by making the area of the cross-section proportional 
to the stress acting on it, or having the cross-sections variable 
in size. 

Represent by 

A, the area of the variable cross-section ; 

A', the area of cross-section at B, or the lower one ; 

A", the area of cross-section at A, or the top section ; 

T,, the strain allowed on the unit of area ; 

W, the force applied to the bar producing elongation; 

x, the distance, B C, estimated upwards from B. 



TENSION. 



87 



The total force acting on any 
section as C, to elongate it, is 



|i iiHiiiiiiiiiiiiiiiiiiiiiiiimiiiiiiiiiiiiiiiiniiiiii»iniiiinmmniniiii 



W+wf. 



Adx % 



w being the weight of the unit 
of volume of the bar. 

Since T 1 is the strain allowed 
on the unit of area, T,xA will 
represent the total strain on 
the section at C, and will be 
equal to the force acting on this 
section to elongate it. Hence, 
we have 

W+wfAdx = T l A (8) 

Differentiating, we have 
wAdx = T^A, 
which may be written 
wdx_dA 

"tT~"a' 

Integrating, we get 

wx 

Tfr =Nap. log A+C. . 




Fig. 14. 



(9) 



Making x = 0, we have A = A', whence 

O^JNap. log A' + C. 

Substituting for C in eq. (9) its value obtained from the 
last equation, we get 

^s = E~ap.log— 
and passing to the equivalent numbers, 



But 
which substituting gives, 



A = A'eTi. 



W 

A'— — -. 
A- T , 



A = JLsTj 



88 CIVIL ENGLNEEKINa. 

Making x — L and A becomes equal to A", hence 
A"- W t 
the value for the area of the section at the upper end. 

Form of bar "when it has a circular cross-section. 

163. No particular form has been assigned to the cross sec- 
tion of the bar in this discussion. Let it be a circle and rep- 
resent the variable radius by r. * 

Then the area of any cross-section will be ttt" 2 , which being 
substituted for A in eq. (8), gives 



W + w I Trr*dx = T x irr*. 



Differentiating, 


there obtains 








W7rr*dx — 


: T,2 irrdr, 


hence 




dr 
r 


W /7 

2t; ' 




which integrated 


gives 










Nap. 


log. r 


w 


+ c, 



• (10) 

which shows the relation between x and r. 

Eq. (10) is the equation of a line, which line being con- 
structed will represent by its ordinates the law of variation of 
the different cross-sections of the bar. It also shows the kind 
of line cut from the bar by a meridian plane. 

The most useful application of this problem is to determine 
the dimensions of pump-rods, to be used in deep shafts, like 
those of mines. 



COMPRESSION. 

164. The strains caused by pressure acting in the direction 
of the axis of the piece tend to compress the fibres and shorten 
the piece. 



COMPRESSION. 89 

From the principle that all bodies are elastic, it follows 
that all building materials are compressible. 

Within the limit of elasticity it is assumed that the resist- 
ances to compression are the same as tension. They are not 
really the same ; but within the elastic limit the differences 
are so small, that for all practical purposes it is sufficiently 
exact to consider them ecpial. 

The coefficient of elasticity of the material is assumed the 
same in both cases, and to distinguish it from the coefficients 
of elasticity when the fibres are displaced in other ways, it is 
sometimes called the coefficient of longitudinal elasticity, 
or resistance to direct lengthening ^1 shortening. fV < 

It is evident that the problems that have been discussed 
for tension are the same for compression, and the solutions 
are alike, except w T e must give a different sign to the applied 
forces, to show that they act in the opposite direction. 

To ascertain the force under which a given piece would be 
crushed, we first ascertain the weight necessary to crush a 
piece of the same material ; and since experiment has shown 
that the resistances of different pieces of the same material to 
crushing are nearly proportional to their cross-sections, the 
required force can be easily determined. 

Assuming that these resistances are directly proportional 
to the cross-sections, let W be the required force, A the area 
of cross-section of given piece, and C the force necessary to 
crush a piece of the same material whose cross-section is 
unity. 

We have, W' : C :: A:l, or 

W = AC, (11) 

hence " ^ = (12) 

Many experiments have been made on different materials 
to find the value of C, and the results tabulated. If the ex- 
periments for finding C were not made on pieces whose 
cross-sections were unity, they were reduced to unity by 
means of eq. (12). The pieces used in the experiments 
were short, their lengths not being more than five times their 
diameter. 

This value of C therefore is the pressure necessary to crush 
pieces whose lengths do not exceed five times their diameter, 
and whose cross-section is unity. It is called the modulus of 
resistance to crushing. 

165. The following are the values of C for some of the ma- 



90 CIVIL ENGINEERING. 

terials in common use, and were obtained by crushing pieces 
of small size, and as a rule not longer than twice their diame- 
ter : 

Material. Crushing Forces per sq. inch, in lbs. 

Ash 4,475 to 8,783 

Chestnut 5,000 

Cedar 5,970 

Hickory. 5,492 " 11,213 

Oak, white 5,800 " 10,058 

Oak, live 6,530 

Pine 5,017 " 8,947 

Fir 6,644 " 9,217 

Hemlock . 6,817 

Cast iron 56,000 " 105,000 

Wrought iron 30,000 " 40,000 

Cast steel 140,000 " 390,000 

Brick 3,500 " 13,000 

Granite 5,500 " 15,300 

Rankine gives from 550 to 800 for common red brick, and 
1,100 for strong red brick. 

The remarks relative to the specimens of wood used to 
obtain the values of T in the table on page 83 apply equally 
to this case. 



SHEARING STRAINS. 

166. There are two kinds of shearing strains ; one a 

transverse, like that caused by punching a hole in a piece of 
metal, or like the strain upon a rivet in riveted plates 
when the plates are subjected to tension or compression ; 
and the other a longitudinal strain, which is resisted by the 
lateral adhesion of the fibres and which is ordinarily termed 
detrusion. 

The relations between the displacements and the forces 
causing them are expressed by formulas analogous to those 
used in the case of elongation. 

In illustrating this strain, the consecutive plane C D (Fig. 
15), is supposed not to have rotated around any line in 
its plane, but to have had a motion of translation parallel to 
the plane A B, so that after the movement any fibre, as ab, will 
have a new position, as ab' . 



A C 



SHEARING STRAIN. 91 

Suppose A B to have remained fixed, and represent by 

L, the original length of any fibre 
ab between the two consecutive planes 
A B and C D ; 

y, the distance bb' which every point 
of the plane C D has moved in the 
direction of C D, relatively to the " b o 

plane A B, owing to the force causing Fig. 15. 

this displacement ; 

s, the amount of shearing force on any fibre ; 

a, the area of the cross section of any fibre ; 

G, a constant. 

Now, in the displacement of ab from the position ab to ab', 
it may be assumed from analogy, that the resistance to this 
displacement is, on the one hand, proportional to the cross- 

ry 

section a ; and, on the other, to -y-, which is the measure of this 

displacement referred to the unit of length. To express the 
hypothesis there obtains 

s = Ga-j- (13) 

in which G may be considered either as constant for any ele- 
mentary fibre, or as variable from one fibre to another. In 
either case there obtains 



■=G 



L 

which is the quotient obtained by dividing the shearing force 
on the unit of area of any fibre by the displacement of this 
area corresponding to a unit of length, and is analogous to 
eq.(l). _ ... 

Within the limit of elasticity, this quotient is constant for 
each elementary fibre. This force G is called the coefficient of 
lateral elasticity, to distinguish it from that of longitudinal 

E 
elasticity. Experiment shows that -fr differs but little from 3. 

If we represent by S, the entire resistance to this displace- 
ment of the plane CD; by A its area ; and assuming G as 
constant throughout its area, there obtains 

S,= GA-g-, •••• (W) 



92 CIVIL ENGINEERING. 

which expresses the relation between the total displacement 

of the section and the force producing it. 

This has been considered as within the limit of elasticity. 

If the force be increased until rupture takes place, we find 

that the resistance will vary for both kinds directly with the 

section, and if S' be the force shearing the bar, we have 

S' 

— — = S, the resistance which the material offers per unit 
A r 

of section to being cut apart by a shearing force. 

Hence S' = AS, in which S is the modulus of shearing. 

167. Values of S have been obtained for several materials, 
some of which are as follows : 

Metals — Values of S. 

Cast steel 92,400 lbs. 

Wrought iron 50,000 " 

Cast iron 30,000 " 

Copper 33,000 " 

Wood — Transverse shearing-. 

Pine. 500 to 800 lbs. 

Spruce 600 " 

Oak (treenails) 3,000 " 

Longitudinal shearing. 

White pine 480 lbs. 

Spruce 470 « 

Fir 592 " 

Hemlock 540 * 

Oak 780 « 



TRANSVERSE STRAIN. 

168. Extraneous forces acting on a piece either obliquely 
or perpendicularly to its axis produce a transverse strain in 
the material. This strain is one of the most common and 
most important to which building materials are subjected, and 
for which the greatest number of experiments have been made. 

Let it be required to determine the relations between 
the force producing deflection and the corresponding 
elongations and compressions of the fibres of a bar, the 
cross-section being uniform and symmetrical with respect to 
the plane through the axis of the bar, and in which the force 
acts. 



TRANSVERSE STRAIN. 



93 



In this case, we assume that the cross-section of the parts 
are either uniform, or else vary by insensible degrees, by a 
law of continuity from one point to another ; the figures of 
the cross-section,, at any two points at finite distances apart, 
being similar, but regarded as the utiiiie bUtWUen any two 
sections infinitely near each other. 

Intersecting the bar by consecutive planes of cross-section, 
the hypotheses adopted are: 

1st. That these planes will rotate around some line drawn 
across the figure of the cross-section. 

2d. That they will remain normal to the fibres after deflec- 
tion. 

3d. That the fibres lying on one side of this line of rotation 
will be extended and the other compressed. 

4th. That the elongation or compression of any fibre will 
be proportional to its distance from this line. 

5th. It follows that there is between the extended and com- 
pressed fibres a surface which is neither extended nor com- 
pressed, but retains its original length, which surface is called 
the neutral surface. 

6th. That the beam will rupture either by compression or 
extension when the modulus of rupture is reached. 

Suppose a bar whose length is great compared with the di- 
ameter of its cross-section, to be placed in a horizontal position, 
one end firmly fixed and the other acted on by a force to 
bend it. 



Bg.A 



c c 



tt— b 



!/ D ' D 



Fig. 16. 



>w 




Fig. 17. 



Let Fig. 16 represent the longitudinal section through the 
axis of this bar cut from it by the plane of the force W, and axis 
E F. This is a plane of symmetry. It will cut from the neutral 
surface a line, which, from the hypothesis just given, will be 
neither extended nor compressed. 

Let E F be this line, which is called the neutral or mean 



94 CIVIL ENGINEERING. 

fibre. Let A B and C D be two consecutive planes of cross- 
.section. Supposing A B to remain in its original position, let 
C D' be the new position assumed by C D with respect to A B 
after deflection. Since these planes make an angle with each 
other, they will intersect in a line, which will be projected on 
the plane of section at some point as R. This point is the 
intersection of the two normals A R and C R to the line E F 
after deflection, and therefore the line R 0' will be the radius 
of curvature for the mean fibre at the point 0'. 

Let Fig. 17 represent the cross-section cut from the bar 
by the plane A B, which is perpendicular to the fibres of the 
bar. Let P be the line cut out of the neutral surface by the 
plane of cross-section. This is the line in the plane around 
which rotation is caused by the deflecting force, and is termed 
the neutral axis of the section. 

Let Y and OZ be. two rectangular co-ordinate axes to 
which all points of the cross-section are referred. 

Represent by 

y and 2, the co-ordinates of all points in the plane Y Z ; 

x, the distances measured on the line E F ; 

dx — Q'o = the distance between the sections A B and C D ; 

dydz = a — the cross-section of a fibre ; 

X — bc — the elongation or compression of any fibre as ab ; 

p — O'R, the radius of curvature. 

It is assumed that the strain is within the limit of elasticity. 

From hypothesis, any fibre, as ab contained between the 
two consecutive planes and above the neutral surface, will be 
elongated by an amount bo proportional to its distance from 
the line P, which elongation is represented by X and the 
distance by y. 

From the similar triangles bOc and O'R (Fig. 16), we have 

bo : O'o, or its equal, ab : : bO : O'R, or X : dx : : y : p, 

hence X z=z~^-dx (15) 

P 
Substituting \ for I and dx for L, in eq. (3), we have 

to be the general expression for the amount of force acting on 
the fibre ab to produce the elongation be. Substituting in this 
for A, the value of a, and for \, its value just determined in 
terms of y, we have for the stress on ab, 

^ydydz (16) 



TRANSVERSE STRAIN. 95 



« 



Therefore the total stress on the fibres elongated will be 
expressed by 

jffydydz. 

In like manner the total stress on the compressed fibres will 
be expressed by 

_ jff ydyd3 > 



the negative sign being used to denote the contrary direction 
of the elastic resistance of the compressed fibres. 

As these strains are caused by the force W acting to deflect 
the bar, and therefore to produce rotation about any neutral 
axis, as P, with a lever arm of F = a?, there will obtain, to 
express the conditions of equilibrium of the system of forces, 



f//^^+f//^^-^=0, . (17) 



that is, the algebraic sum of the moments of the extraneous 
forces is equal to zero. 

Since the resistance developed in each fibre is exactly equal 
and contrary to the force acting upon it to produce elonga- 
tion or compression, eq. (17) shows that the sum of the mo- 
ments of resistances in any section is equal to the sum of the 
moments of the extraneous forces. 

In this particular case, the neutral axis divides the cross- ] 
section symmetrically and the centre of gravity coincides with J 
the centre of figure. Let b be the limiting value of 2, and a? 
of y, then eq. (17) may be written J 







i 



dydz=(wx\ . . (18) 



The quantity— ify'dydz is dependent upon the form of 
cross-section and nature of the material. The quantity / / 

y*dydz is the moment of inertia of the section C D with 
respect to the right line drawm through the centre of gravity 
of the section, and perpendicular to the plane passing 
through the axis of the bar and of the force W, In this 



96 CIVIL ENGINEERING. 

case, this right line has been shown to be the neutral axis 
of the section. Representing this moment by I, eq. (18) may 
be written 

— =JWX)^UIL • • (19) 

p ' 

The first member is oftentimes called the moment of elas- 
ticity, sometimes the moment of resistance, and at others 
the moment of flexure, and the second member is called 
the "bending moment. 

169. Eq. (18) may be verified as follows : 

From Analytical Mechanics, we found that if all the ele- 
mentary masses were concentrated at a point, called the prin- 
cipal centre of gyration, the moment of inertia would be un- 
altered ; also, that the forces tending t© produce rotation of 
the body might be concentrated at this point, without there- 
by changing the conditions of equilibrium. 

Let W be the extraneous force, acting with a lever arm x, 
tending to produce rotation of C D around some lin^ in it ; 
suppose the resistances, offered by the fibres to rotation, con- 
centrated at the principal centre of gyration, and equal to P' 
acting with a lever arm, k. 

We have for equilibrium, 

From Mechanics, we have 

2mr 2 



k = principal radius of gyration = A / — r- 



in which m is the elementary mass, r its distance from the 
axis, and A the area of cross-section. 

Referring the elements of the cross-section to the co-ordi- 
nate axis of Y and Z taken in its plane, as shown in Fig. 16, 
and substituting the sign of integration for 2 and for m, its 
value in terms of y and z, we get, 




, fftfdydt 



A 

Squaring and dividing both members by k, we get 

J Jy*dydz 



AJc 



TRANS VEKSE STRAIN. 97 



Hence, 



and 



whence 



p,_ (Wxj xAk 
J ' ftfdydz 

P' ifcx) 



(20) 



A 



J ' ftfdyds. 



which is the value the force would have on the unit of area 
at the principal centre of gyration, or the distance Jc from the 
neutral axis, under this hypothesis. 

It has been assumed that the resistances are directly pro- 
portional to the distance from the neutral axis; hence, at the 
unit's distance, the force on the unit of area would be 

P' (Wx) 

** ~ fffdyd7 

and at the distance, y, the force would be 
Yy W^/ 



AJc 



f ftfdydz 



The strain on the unit of area at the distance, y, from the 

E 
axis is shown by expression (16), to be equal to — y- Hence, 

r 



P 

or 



E Wxy 

y 



f fy'dydz 
ffy*dydz=Wx, 



P 
which is the same result as that shown by eq. (18). 

7 






98 CIVIL ENGINEERING. 



SHEARING STRAIN PRODUCED BY A FORCE ACTING TO BEND THE 

BAR. 

170. No reference was made in the preceding article to 
the shearing strain produced in the bar by a bending force 
acting at one end, for the reason, that in prismatic bars of 
this kind it is rarely necessary in practice to consider this 
strain. 

If in this bar (Fig. 16), the section A B had been taken 
consecutive to the end section, the one at F, where the force 
was applied, the action of the force would not have been to 
turn this section F around a line in its plane, but to have 
sheared it off from its consecutive section. This action would 
have been resisted by the adhesion of the sections to each 
other. The force W is supposed to act uniformly over the 
entire section F, hence the resistance to shearing in the 
adjacent section will be uniformly distributed over its sur- 
face and equal to W. The resistance on the unit of surface 

W 

would therefore be -r— 
A 

The adhesion of these two sections prevents their separa- 
tion by this force, hence the second section is drawn down by 
the force W, which tends to shear it from the third section, 
and so on. 

In this particular case, the action of the force W to shear 
the sections off, is transmitted from section to section until 
the fixed end is reached, and the shearing strain of each sec- 
tion is the same and equal to W. And in general, the shear- 
ing steain of any cross section of a bar or beam placed in 
a horizontal position is equal to the sum of all the vertical 
forces transmitted through and acting at that section. 



CHANGES IN FORM OF THE BAR. 

171. The lengthening and shortening of the bar produced 
by a force acting in the direction of its axis have been the 
only changes of form considered. There is another that in- 
variably accompanies them. This is the contraction or en- 
largement of the area of cross-section, when the bar is ex- 
tended or compressed. When the elongation or contraction 
is small, the change in cross-section is microscopically small ; 
but when these strains are very great, this change is sensible 
in many materials. 



TRANSVERSE STRAIN. 99 

In structures, the pieces are not subjected to strains of 
sufficient magnitude to allow this change of cross-section to 
be observed, and hence it is neglected. 

It is well to keep this change in section in mind, as by it 
we are able to explain certain phenomena that are met with 
in experiments, when the strains to which the specimens are 
submitted pas£ the limits of elasticity. 



STRAIN ON THE UNIT OF AREA PRODUCED BY A BENDING FORCE. 

172. Expression (16) represents the stress of extension on 
the fibre whose cross-section is dydz. Dividing this expres- 
sion by the area of cross-section of the fibre, we have 

i,-p. 

in which P represents the stress on the unit of area at the 
distance y from the neutral axis. Dividing through by y 
and multiplying both members by I, we have 




== jWz) .... (21) 



EI__PI 

p ~ y 

whence 

P=^4 (22) 

which formula gives for a force of deflection, the stress on a 
unit of area at any point of the section. 

The bar has a uniform cross-section, I will therefore be 
constant, and the value of P will vary directly with W ftiMsLflg/ W)CJ 
and by giving to y its greatest value, we find the greatest- 
strain in. any assumed cross-section. 



VALUES OF I. 

173. In bars or pieces having a uniform cross-section, the 
moment of inertia for each section with reference to the neu- 
tral axis is the same, and hence I is constant for each piece, 
and is easily determined when the section is a known geomet- 
rical figure. 



100 



CIVIL ENGINEERING. 



1. When the cross-section is a rectangle (Fig. IS) 
in which b is the breadth, and d the depth, the 
integral taken within the limits z = 0, and z — b. 
y — \d and y — — ^d, gives 



1 = 



bd" 



Fig. 18. 



2. For a cross-section of a hollow girder, like that 
of (Fig. 19) in which b is the entire breadth, d the total 
depth, b' the breadth of the hollow interior, df its depth, the 
integral gives 






Fig. 19. 

the limits 
+ , and — 



1 = 



(bd s — b'd' z ) 



The expression will be of the same form in the 
case of the cross-section of the I-girder, (Fig. 
20), in which b is the breadth of the flanges ; b' 
the sum of breadths of the two shoulders ; d the 
depth of the girder, and d' the depth between the 
flanges. 

3. When the cross-section is a circle, and the 
axes of co-ordinates are taken through the centre, 
of z will be + r, — r ; and those of y will be 
Vr 2 — z 2 ; and 



A 



* 



I = \itt\ 

4. For a hollow cylinder, in which r is the 
exterior and r' the interior radius, 

I = J *■(*•* — *•")• 

5. When the cross-section is an ellipse, and 
the neutral axis coincides with the conjugate 
axis, if the transverse axis be represented by d, 
and the conjugate by b, and the limits of z and y 



Fig. 20. 
be taken in the same manner, as in the circle, then 



6. When the cross section is a rhombus or lozenge, in 
which b is the horizontal and d the vertical diagonal, 

I = AW». 



FLEXURE. 



174. In the preceding article on transverse strain, to sim- 
plify the investigation, without affecting the accuracy of the 



FLEXURE. 101 

results, the bar was placed horizontally, and no notice was 
taken of the change of position of the mean fibre after the 
application of the bending force. 

The strain was within the limit of elasticity, and for this 
force the body was regarded as perfectly elastic. 

The action of the force was to bend the bar, and hence to 
bend the mean iibre without lengthening or shortening it, 
making it assume a curved form. 

When the bar is bent in this manner, the curve assumed 
by the mean fibre is called the elastic curve or equilibrium 
curve. Its equation is deduced by equating the moment of 
resistance and the bending moment, and proceeding through 
the usual steps. 

All the external forces to the right, or to the left, of any 
assumed cross-section are held in equilibrium by the elastic 
resistances of the material in the section. 

EI r 

The general equation (19), — =£Way expresses the condi- 
tion of equality between the moments of resistance and bend- 
ing, and is the equation from which that of the curve as- 
sumed by*the mean fibre after flexure may be deduced. 

From the calculus, we have 

which, substituting in eq. (19), gives 

£#*■ :■.■■« 

in which x is t he lev er a?m^f- tfoe- i -a i pp l liod i&ve^ yWMj 

Regarding the deflection as very small, -Jl, which is the 

square of the tangent to the curve at the point x, y, may be 
omitted, and eq. (23) becomes for this supposition 

Elg=W^ (24) 

which is the general equation expressing the relation between 
the moment of flexure and the bending moment of the ex- 




102 CIVIL ENGINEERING. 

traneous forces for the mean fibre of any prismatic bar, when 
the deflection is small. 

175. To find the equation of mean fibre in ease of a 
bar placed horizontally, fixed at one end and acted upon 
by a force W at the other. 

Denote by (Fig. 21) 
Z, the length of the bar 
from the fixed end to 
the point of application 
of W , it will be equal -* 
to the length of the 
mean fibre, A B. 

Let AX and AY be 
the co-ordinate axes 

and Y positive downwards. The bending moment of W for 
any point, x, will be W (I — x), and substituting this for Wx 
in eq. (24), we have 

Integrating, we have 

dy W 
El dt = 2T(2&-<*) + C. • • (26) 

If x — 0, by hypothesis ~ = 0, and hence C = 0. 

CLX 

Integrating eq. (26) we have 

Ely = ~ {ZU — a*) + C . . (27) 

Noting that for x — 0, y = 0, we have C = 0, 

W 

hence, y = —==- {ZM — X s ) . . . (28) 

which is the equation of the curve of mean fibre under these 
circumstances. 

Inspection of eqs. (26 and 28) will show that the greatest 
slope of the durve and the greatest distance between any 
point of it and the axis of X will be at B. Eq. (25) shows f 
that the curve is convex towards the axis of X. 

Represent by f the maximum ordinate of the curve. Its 
value will be obtained by making x = I, hence 

AVZ 3 
/=3ET 0°> 



STRAINS IN BEAMS. 103 

If the bar had been loaded uniformly instead of by a 
weight acting at its extremity; representing by w the load 
on a unit of length, eq. (24) would have become for this case, 

Elg = ! (*-,)* . • • • (30) 
hence the equation of the curve of its mean fibre, 

w 

The value of the maximum ordinate in this case would be 

f-m » 

Instead of W concentrated at the end as shown by eq. 
(28), suppose it to have been uniformly distributed over the 

W 

bar, then — - would be the load on each unit of length in that 
c 

case, and substituting this in eq. (32) for w, and calling the 

corresponding ordinate, f\ we have, 

/' = StfT ~ S^T * * ' ( 33 ) 



Hence y if'.'.i'-i, from which we see that concentrating 
the load at the end of the bar increases the deflection nearly 
three times that obtained when the load was uniformly dis- 
tributed. 



BEAMS OF UNIFORM CROSS-SECTION. 
BEAMS RESTING ON TWO OK MORE SUPPORTS. 

176. By the term, bar, used in the previous discussions was 
meant any piece, the diameter of whose cross-section was 
small when compared with the total length of the piece. 

If the bar is of considerable size and has a cross-section of 
several square inches or more, the term beam is applied. 
When the beam rests on two supports and is subjected to a 
transverse strain, it is usually called a girder. If it be 
placed ^n. a horizontal position, with one end fixed and the 
other free, it is known as a semi-girder or cantilever. 




104 



CIVIL ENGINEERING. 



'£v*y 



^W 






BEAM RESTING ON TWO POINTS OF SUPPORT. 

177. Let it be required to determine the bending mo- 
ments, shearing straiiv and equation of mean fibre of a 
straight beam resting in a horizontal position on two 
points of support. 

There are two cases : 1, when the beam is uniformly loaded ; 
and, 2, when acted upon by a single force, yf, between the 
two* points of support. 

1st Case. — The external forces acting on the beam are the 
load uniformly distributed over it and the vertical reactions 
at the points of support. 



AWK, 



f-WR.x 



ffl '/// 



Fig. 22. 

Let A B (Fig. 22) be the beam, A and B the points of sup- 
port, and A the origin of co-ordinates. A X and A Y, the axes. 
Denote by 21 the distance between two points of support A B. 

w — weight on unit of length. 

x = abscissa of D, any section of the beam A B. 

The total load on the beam is 2wl and the reactions at each 
point of support are respectively equal to — wl. 

Bending moment. — Let D be any section of the beam made 
by a plane passed perpendicularly to the axis, through the 
point, whose abscissa is x, and let us suppose either segment 
to be removed ; in this case let it be B D. 

The forces acting on the remaining segment A D are the 
weight on this portion of the beam, and the reaction at A. 
The algebraic sum of their moments will be the bending 
moment of the external forces acting on this segment. Let 
M be this moment and we have 



x wx 7 . 

M = wx x-^-wlx x= — wlx . . . (34) 



STRAINS IN BEAMS. 105 

The second member of: this equation is a function of a sin- 
gle variable, and may therefore be taken as the ordinate of a 
line of which x is the abscissa. Constructing the different 
values of the ordinate, the line may be traced. This line-is a 
parabola, and shows the rate of increase or decrease in the 
bending moments. 

The curve thus constructed may be called the curve of the 
bending moments. , 

Shearing strain. — The shearing s4min on the beam at D ^ 
is equal to the algebraic sum of all the vertical forces acting 
at this section, hence 

S' = wx — wl (35) 

The second member of this equation represents the ordi- 
nate of a right line. Constructing the line, the ordinates will 
show the rate of increase or decrease of the shearing strain 
for the different sections. 

By comparing equations (34) and (35) it will be seen that 

S'=^ (36) 

which shows that the shearing strain at any section is ^' ] * 

equal to the first differential coefficient of the tending moment 
off that section taken with respect to x. 

For convenience we used the segment A D, but the results 
would have been the same if we had taken B D. For, sup- 
pose we find the bending moment for this segment, we have 
for the moment of the weight, acting to turn it around B, 

W (2l -x)x ??=? = ^(2Z - x)\ 
2 2 

And for the moment of reaction, 

- wl(2l - x). 

The algebraic sum of these moments will be 

wx* 7 
wlx, 

2 

the same as (34), as it should be. 

Equation of mean fibre. — Substituting the second mem- 
ber of eq. (34) for ^Noy'vn eq. (24), we have 

EI^l = ^x'-wlx. . . (37) 
dx 

Integrating, we get 

^jlv w 3 w, „ 



ff 



106 CIVIL ENGINEERING. 

For x = L -JL = 0, and we have C = hvl\ 
ax 

Substituting this value of C, and integrating, we get 

Ely = |V_!V+ %wfx + C. 
For x = 0, y is equal 0, and hence G-== 0, and we have 

v=^p-w+&*) - • • ( 38 > 

which is the equation of the curve of mean fibre, and may be 
discussed as any other algebraic curve. 

Deflection. — If we represent the maximum ordinate of the 
curve byy, we find 




the maximum deflection 

the middle point te-bend the beam." 

Equation (38) may be placed under the form, 

w 

y = a®(afiB.-«0[W->-i^ . (39) 

For values of x, differing but slightly from I, the quantity 
(x—lf may be omitted without materially affecting the value 
of the second member for these values. Omitting this quan- 
tity, and eq. (39) reduces to 

2/ = 2lEi(2to-«0 • • • • (40) 

which is the equation of a parabola. Hence, a parabola may 
be constructed passing through the middle point of the curve 
of mean fibre and the points of support, which nearly coin- 
cides with the curve of mean fibre in the vicinity of its 
middle point. 

The parabola whose equation is eq. (40) differs but slightly 
throughout from the curve given by eq. (38) ; for the greatest 
difference between the ordinates of the two lines for the same 

value of x, will be when x = - (2 ± V 2), which gives 

^=2iEl X *'/ = 2iEl X *' 

?/', representing the ordinate of the curve for this value of #, 
and y'\ the ordinate of the parabola for the same value of x. 



STRAINS IN BEAMS. 107 

Whence, we get 



y -y 



= i 



y 

178. 2d Case. — The external forces acting on the beam are 
the applied force, whatever it may be, and the vertical re- 
actions at the points of support. 

Let A B (Fig. 23) represent the beam resting on the supports, 
A and B, sustaining a weight, 2W, at any point, as P, between 
the points of support. Denote the reactions at A' and B by 
R x and R 2 , A B by 2Z, A P by V . 



2W 

Fig. 23. 

The reactions R, and R 2 will be proportional to the segments 
in which the beam is divided, and this sum, disregarding the 
weight of the beam, is equal to 2W. Hence, 

R, : R 2 : 2W ; ; PB : AP : AB, 
from which proportion we, knowing 2W and V, can determine 
the values of R 2 and R 2 . , Knowing these, we can obtain the 
beudiug moment and shearing strain of any section, and the 
deflection of the beam due to the force 2W. 

179. The most important case of the single load is that in 
which the load is placed at the centre. Suppose 2W to act at 
the centre, thenR, =R 2 = W*. Assume the origin of co-ordin- 
ates and the axis of X and Y to be the same as in the first case. 

Bending moment. — The bending moment for any section 
will be M = - Wx. Wu?o*v /r ? *- 

Shearing strain. — The shearing a&mm on any section will be 

S' = ± w. u-.t^ A v c^ 

Equation of mean fibre. — Substituting in second mem- 
ber of eq. (24) the above value of M, we have 

ei S=- w * < 4i > 

Integrating, and substituting for C, its value, we get 
dy W 

™£=-2 <?-<*> • • • • (* 2 ) 



-"W 



108 CIVIL ENGINEERING. 

Integrating again and substituting for C, its value, we get 
W 
y= 6EI (3 ^~* 3) '- - " * (43) 
which is the equation of so much of the mean fibre as lies be- 
tween the origin, A, and the middle point, C. 

The right half of the mean fibre is a curve exactly similar 
in form. Assuming B as the origin and the abscissas as posi- 
tive from-B towards C, eq. (43) is also the equation of the 
right half of the curve. 

Deflection. — The maximum deflection is at the centre, and is 

WZ 3 

Comparing this with the deflection at the centre in the 
previous case, it is seen that the deflection produced by a load 
uniformly distributed over the beam is five-eighths of that 
produced by the same load concentrated and placed at the 
middle point. 

180. Comparison of strains produced. — The bending 
moment for any section, when the beam is uniformly loaded, 
is, eq. (34), 

K = — wlx, 

and when the beam is acted upon by a load at the middle 
point, is, eq. (41), 

M = — Wx, 
Both will have their maximum values for x = I. 
Equating these values, we have 

Wl = iwP, 

whence W = -~-, 

which shows that the greatest strain on the unit of area of 
the fibres, when the load is uniformly distributed, is the same 
as that which would be caused by half the load concentrated 
and placed at the middle point of the beam. 



Beams strained by a uniform load over its entire 
length and a load resting midway between the two 
points of support. 

181. If the beam be uniformly loaded, and support also a 
load midway between the points of support, the corresponding 



STRAINS IN BExVMS. 



109 



values for the strains can be obtained by adding algebraically 
the results determined for each case taken separately. 

If the beam had other loads besides the one at C, we could 
in the same manner find the bending moments, shearing 
strains, and deflections due to their action. The algebraic 
sum of the moments, ordinates of deflection, etc., would give 
the •results obtained by their simultaneous action. 



Beam having its ends firmly held down on its sup- 
ports. 

182. In the preceding cases the beams are supposed to be 
resting on supports, and not in any way fastened to them. 
If the ends of the beams had been fastened firmly so that 
they could not move — as, for example, a beam having its ends 
firmly imbedded in any manner in two parallel walls — the 
results already deduced would have been materially modified. 

Let it be required to determine the strains and equation of 
curve of mean fibre in the case where the beam has its ex- 
tremities horizontal, and firmly embedded so that they shall 
not move, the beam being uniformly loaded. 

If we suppose a bar fitted into a socket (Fig. 24) and acted 
upon by a force to bend it, it is evident, calling Q t the force 
of the couple developed at the points B and H, that the mo- 
ment of the force W, whose lever arm is Z, is opposed by the 
moment of resistance of the couple, B Q t and H Q x acting 
through the points H and B. 



Pit 




Fig. 24. 



Hence, we have 



QJ' = IW, 
I' being the lever arm of the couple. 



110 



CIVIL ENGINEERING. 



We see that Q t increases proportionally to any decrease in 
l r , and that these quantities themselves are unknown, although 
their product must be constant and equal to the bending mo- 
ment of the beam at B. 

To determine the bending moment at any section of a beam 
having its ends firmly held down ; let A B (Fig. 25) be the 
beam before being loaded, and denote by 

21 = A B = the length ; 

w = the weight on unit of length ; 

x — the abscissa at any point, the origin of co-ordinates 
being at A, and A B coinciding with axis of X, as in preced- 
ing cases. 




The total load on the beam will be 2i#Z, and the reactions 
at the points of support are each equal to — wl. 

The bending moment of any section D, is equal to the 
algebraic sum of the moments of vertical reaction at A, of 
the weight on A D, and of the unknown couple acting on the 
left of A. 

Calling /n the moment of the unknown couple and substi- 
tuting this algebraic sum in eq. (24), we have 

wx 2 






EI 



d&' 



—wlx + ^+fi 
dy 



(U) 



Integrating and noting that for x=0,-r-—0, we have C=0, 
and 



EI 



dy 

dx 



2 + 6 



+ fix. 



(45) 



In this equation make x 



dy 
= 2Z, for which-y-=0, and we find 

ft = $wP, 



STRAINS IN BEAMS. Ill 

which is the value -of the moment of the unknown couple 
acting at the left point of support. It is also the value of 
the one at the right point of support, B. 

Writing this value for fi in equations (44) and (45), we have 

d?y w w 

Yl-^^-wlx+^ + ^V . . . (46) 

^dy wl n w „ wl? /JWV 

and then by integration, 

^^ wl n w , wl 2 „ _, 

Ely =- -Q-a? + Y ^ +-g-a?+C. 

We find C'=0, and substituting, etc., we get 

y = mp-* 1 ? < 48 ) 

which is the equation of the curve of mean fibre. 

Deflection. — Denoting byy, the maximum value for y, and 
we have 

- r -24Er- 

The corresponding value obtained, from eq. (38), is 

f- —I* 

A comparison of these values of f shows that by firmly 
fastening the ends of the beam to the points of support in a 
horizontal position, the deflection at the centre is one-fifth of 
what it was when they merely rested on the supports. 

Bending moments. — The curve of the bending moments is 
given by the equation. 

__ w \ w 

M =—af— wix + -Q-r, 

which is that of a parabola. 

The bending moments for x = 0, and 21, are both equal to 

W IVo 

-Q- Z 2 , and for x = I, — -«-. The bending moment of the 

section at the middle point is therefore half that of the section 

w 
at A or B. Assuming a scale, lay off ~irl 2 , below the line A B, 

on perpendiculars passing through A and B: Lay off half this 
value on the opposite side of the line A B on a perpendicular 



112 CIVIL ENGINEERING. 

through the middle point. This gives us three points of the 
curve of which one is the vertex. The perpendicular through 
the middle point is the axis of the parabola, and with the 
three points already found the curve may be constructed. 

This curve of bending moments cuts the axj.s of X in two 
points, the abscissas of which are I (1 ± 4/ J), and at the 
sections corresponding to them the bending moments will be 
equal to 0. 

These values substituted in eq. (46) for x, reduces-^ 

to zero, and an examination of this equation shows that 

there is a change of sign in -^ at these points. It therefore 

follows that the curve of mean fibre has a point of inflex- 
ion for each of these values of x, that is, the curve changes 
at these points from being concave to convex, or the reverse, 
towards the axis of X. 

The greatest strains on the unit of area produced by the 
deflecting force, will be in the cross-sections at the ends and 
middle ; the lower half of the cross-section at the middle 
being extended, and the lower halves of these at the points of 
the support being compressed. 

Shearing strain. — The expression for the shearing force is 

dK 

b = — ^ — — WX — WO, 

which is the same as eq. (35), and its values may be repre- 
sented by the ordinates of a right line which passes through 
the middle point. 

The uniform load concentrated and placed at the middle. 

183. If instead of being uniformly loaded, the beam wis 
only strained by a single load, 2W, at the middle point, the 
bending moment, disregarding the weight of the beam, would 
be for values of x < I. 

M = — W x + iju 
and by a process similar to that just followed, we would find 

W 

y = i2ET (3 ^ -*^ 

to be the equation of the mean fibre from A to C. 
The maximum deflection will be 

1 ~ 12EI b ' 



STRAINS IN BEAMS. 



which is equal to one-fourth of that obtained, with a load at 
the centre, when the ends of the beam ,are free. It is also 
seen that the deflection caused by a concentrated load placed 
at the middle of the beam, is the same as that caused by 
double the load uniformly distributed over the whole length. 
If the beam was loaded both uniformly and with a weight, 
2W, the results would be a combination of these two cases. 



BEAM LOADED UNIFORMLY, FIXED AT ONE END, AND BESTING ON 
A SUPPORT AT THE OTHER. 

184. Let A B (Fig. 26) represent the beam in a horizontal 
position, fixed at the end, A, and resting on a support at the 
end B. 



.\l 




Fig. 26. 

Adopting the notation used in previous case, we have %wl 
for the total load on the beam. 

The reactions at A and B are unequal. Represent by R x 
the reaction at A, and by fi the moment of the unknown 
couple at A. We have 

Elg = -E 1 c 8+ ^ + /4 . . (49) 



Hence by integration, 



EI ^ = - |E^ 8 + -f- x* + fix, C = (50) 



w 



EIy=-jE,»'+gj(«'+A» T ,O'=0 (51) 

The bending moment at B is equal to zero, hence for 

x = 21, y will be and the first member of eq. (49), 0. 

w 
Hence = - K X 2Z + -^ (2Z) 2 + fi . ., . (52) 

w 
ml*q. (51), = - * R,(2Z) 8 + ^ (9/)* + /m \ (21)' . (53) 



J 



114 



CIVIL ENGINEERING. 



Combining these we find 



^=•1 w (21) and fi = 



wl* 



Hence the reaction at B is %w (21). 

Substituting these values for R x and fju in eq. (49) the bend- 
ing moment at any point, shearing strain, and curve of mean 
fibre can be fully determined. Placing the second member 
of eq. (49) equal to zero, ana deducing the values of x, these 
will be the abscissas of the points of inflexion, and by placing 
the second member of eq. (50) equal to 0, the abscissa cor- 
responding to the maximum ordinate of deflection may be 
obtained. The curve of bending moments, etc., may be de- 
termined as before. g n \J, 

1 ul*'™* *'*/*£*(*■ 






BEAM RESTING ON THREE POINTS OF SUPPORT EST THE SAME 
HORIZONTAL STRAIGHT LLNE. 

185. Let it be required to determine the bending moments, 
shearing strain, and equation of mean fibre of a single 
beam resting in a horizontal position on three points of sup- 
port, each segment being uniformly loaded. 

Let ABC (Fig. 27) be the beam resting on the three points, 
A, B, and C. 



t, 



•v- 



Fig. 27. 



?. 



Let us consider the general case in which the segments are 
unequal in length and the load on the 'unit of length dif- 
ferent for them. 

Let I = A B, and w, the weight on each unit of its length, 
l'= B C, and w' the weight on each unit of its length. 

Rj, R 2 , R 3 , the forces of reaction at the points of support, 
A, B, and C, respectively. 

Take A B C as the axis of X and A the origin of coordinates 
with y positive downwards as in the other cases. 



First, consider the 



segment A B, and let D be 



any 



section 



whose abscissa is x. 

Since the reactions at the points of support are unknown, 
they must be determined. 



STRAINS IN BEAMS. 115 

We have 

"3.--W? • • • <«> 

Integrating, we get 

Let ^ represent the angle tnade by the curve of mean fibre 

with the axis of X at A, then for x — we have I -j- \ =tan <f>, ^ 

whence EI tan. <£ = C, which substituting and transferring 
to the first member, may be written 

Elg-tan</>) = -£K^+^. (55) 

Integrating again, we get 

wx 
EI(y-*tan^)=-^E 1 ar'+ ^-, . (56) 

the constant of integration in this case being equal to 0. 

If in eq. (54) we make x = I, and denote the bending mo- 
ment of the section at B by //-, we have 

11)1 

M =-^ + T - .... (57) 

Make x = I, hence y = 0, in eq. (56) and we have 

EI tan (/> - i^ +TkwP= . . (58) 

by omitting common factor I. Combining this equation with 
the preceding one and eliminating K^ and reducing, we get 

llfi + EI tan <t>--^\wl s = . . (59) 

In eq. (55) make x = I and denote by co the angle made by 
the mean fibre at B, with the axis of X, and we have 

EI (tan co - tan <f>) = - i^LJ? + \wV . (60) 

Combining this and equation (57) and eliminating R x we 
have 

EI (tan co - tan <f>) = \ Ip - T V wl 3 . (61) 

Combining this with eq. (59) and eliminating tan cf> we 
have 

EI tan a) = i Ifi, - -z\wP . . (62) 

which expresses the relation between the tan co and fi. 

Going to the other segment, taking C as the origin of co- 
ordinates and calling x positive towards B, we may deduce 



116 CIYTL ENGINEERING. 

similar relations between the bending moment at B and the 
tangent of the angle made by the mean fibre at B with the 
axis of X. Since the beam is continuous, these curves are 
tangent to each other at the point B, and the angles made by 
both of them with the axis of X at that point are measured by 
a common tangent line through B. Therefore, the angles are 
supplements of each other and we may at once write the cor- 
responding relation as follows, 

-EItana)=^V-%V'^' 3 .... (63) 
Since, for equilibrium, the algebraic sum of the extraneous 
forces must be equal to zero, we have 

wl+wT—R i —R 2 —R B =0 . . . (64) 

and since the algebraic sum of their moments with respect to 
any assumed section must be equal to zero, we have for the 
moments taken with respect to the section at B, 

V^xl+w'l'x^ = R,xl' + wlx~. . .(65) 

These four equations, (62), (63), (64), and (65) contain four 
unknown quantities, Ri, R 2 , R 3 , and tan co. 

By combining and eliminating, their values may be found. 
Combining equations (62) and (63), and eliminating tan o>, we 
have 

_ x wl B + w'V* 

The bending moment of any section, as D, is from equa- 
tion (54) 

— Rjpa + w—; 

hence for x = I, we have M equal to the bending moment at 
B, which has been represented by /a, or eq. (57) 



/*= 


-RiZ + 


W 72 


t 
wl 

~2 


fl wl 


f 1(1 + 1') 



from which we get 

Rl = ^-7=if -i f(7T7r - (66) 

In a similar way, the value of Eg may*be found. These 
values of ll x and Rj substituted in eq. (64), will give the value 
of R.,. 



STRAINS IN BEAM'S. 117 

The external forces, all being known, the bending moments, 
shearing strain, and equation of mean fibre may be deter- 
mined as in previous examples. 
-A-1S6. Beam- resting in a horizontal position on three 
^points of support, the segments being equal in length and 
the uniform load on the unit of length being the same. 

The most common case of a beam resting on three points 
of support, is the one in which the beam is uniformly 
loaded throughout and the intermediate support placed at the 
middle point. 

In this case, I = Tand w = w. Substituting these values, in 
the expressions for //, and R 1? w T e have 

/a =. -§- wP, and Hi = §tvl. 

The reaction at the middle point will therefore be 

±±ivl or fiv(2l). 

In the case of a beam resting on two supports, Fig. (22), and 
having a weight uniformly distributed along its length, it has 
been shown that each support bears one half the distributed 
load ; and that the deflection of the mean fibre at tlie middle 
point, represented by f is the same as the beam would taivvj 
were fths of the load acting alone at the middle point. In 
the latter case the pressure upon a support, just in contact 
with the beam at its middle point, would be zero ; and if the 
support were to be raised so as to bring the middle of the 
l^eam into the same right line with the extreme supports, the 
intermediate support would evidently counteract the total 
pressure at C to which the deflection was due, and which was 
fths of the entire load ; hence the reaction of the middle sup- 
port will be equal to -fths. This conclusion agrees with the 
result determined by the previous analysis. 

Each segment of the beam in this case might have been 
regarded as a beam having one end fixed and the other rest- 
ing on a support; a case which has already been consid- 
ered. 



THEOEEM OF THREE MOMENTS. 

187. From the preceding, it is seen, that the reactions at 
the points of support can be determined whenever we know 
the bending moments at these points. These moments are 
readily found by the " theorem of three moments." 

This theorem has for its object to deduce a formula express- 



118 



CIVIL ENGINEERING-. 



ing the relation between the bending moments of a beam. 
at any three consecutive points of support, by means of which 
the bending moments at these points may be obtained, with- 
out going through the tedious operations of combination and 
elimination practised in the last example. 

Take any three consecutive points of support, as A, B, and 

A I B I C 

Fig. 28. 



3 



C, Fig. (28), of a beam resting on n supports. Denote by I 
and V , the lengths of the segments, A B and B C, w and w r , 
the weights on each unit of length in each segment and 
M x M 2 M 3 , the bending moments at these points, A^ B, C. 

The formula expressing the relation between these bending 
moments is 

MxZ + 2M 2 (Z + V) + M/ = iwl 3 + iwT 3 . (67) 

In every continuous beam, whose ends are not fixed, the 
bending moments at the end supports are each equal to zero. 
Hence, by the application of this formula, in any given case, 
as many independent equations can be formed as there are 
unknown moments, and from these equations the moments 
can be determined. 

188. The demonstration of this theorem depends upon the 
principle, that the bending moment at any point of support 
whatever, and the tangent of the angle made by the neutral 
fibre with the horizontal at that point, may be expressed in 
functions of the first degree of the bending moment at the 
preceding point of support, and the tangent of the angle 
made by the neutral fibre with the 'horizontal at that point. 

Let A B (Fig. 29) be any segment of a beam resting on n 
supports, A the origin, A X and A Y the axes of co-ordinates, 
and Mj. and M 2 the bending moments at A and B. 



Fig. 29. 

The applied forces acting on the beam and the reactions 
arc taken vertical and in the plane of the mean fibre. 



A 



»V 7 



STRAINS IN BEAMS. 119 



The external forces which act on the beam to the left of 
the support, A, may be considered as replaced by a resultant 
moment and a resulting shearing force, without disturbing 
the equilibrium. This resultant moment, represented by M 1? 
is equal and opposite to the moment of the internal forces 
at the section through the support A; the vertical force, ' \- 

which we represent by Si, is equal and opposed to the »kca,» - Hv y 

XJBg i'oroo at- this- ooofeMK L *\f\4 &<&*. tf" Aa*<a* * « * «4' £k L+\w(rJ c 
y\ Represent by //, the algebraic sum of the moments of the 
external forces acting on the beam between A and any section 
as D, whose abscissa is x. 

Then from eq. (24) we have 

EI J = M 1 + /t + S li8 . . . (68) 

Denoting by <j> the angle which the neutral fibre after de- 
flection makes with the axis of X, at A, and integrating, we 
have 

EI IM - tan <f>\ = M& + f^dx + JS^. (69) 



Representing the quantity / fidx by M' and integrating, 
we have 

El(y-x tan 0) = ^M^ 2 + / Wdx + JS^. (70) 

J 

In these three equations, make x = I and denote by !N", Q, 

and K what /-t, M', and / Wdx become for this value of x> 
' J 

and by co the angle made by the curve of mean fibre with 

the axis of X at B ; noting that for x = I, EI ^ = M 2 , we 

have 



M 2 = Mi + N + SA 

EI (tan co - tan <£) = M t Z + Q + i$A 

— Ell tan £ = P^Z 2 + K + iS/. 



(71) 






\L • - 



120 



CIVIL ENGINEERING. 



Combining the first and third, and then the second and third 
of these equations and eliminating S 1? we have 



■i-M^ 2 + EB tan <f> = - iM x Z 2 + i^Z 2 - K, 
JEIZ tan co + fEIZ tan <j> = 



fMJ? + iQl 



K 



.1 



(72) 



In these equations, N", Q, and K depend directly upon the 
applied forces, and wheajthey are known t h e se ■ q-tran titres are 
given. But M 1? M 2 , tan <j> and tan co are unknown. 

An examination of equations (72) shows that M 2 and tan co 
are functions of the first degree of M. 1 and tan <p, whatever 
be the manner in which the external forces are applied. 

Let us impose the condition that the system of forces acting 
on the beam shall be a load uniformly distributed over each 
segment, and denote by w the load on a unit of length of the 
segment A B. 

Eor this case we have 



LtA 



i 



M 1 == ±wx z , 



M'dx = 



^;x 



war 



and in these, by making x = ?, we have 



N = \wl\ 

K = i^wlK 

Substituting in equations (72) these values for N, Q, and K, 
we have 



M, 



6"FI 

2M X — -j- tan cj> + \wl?, 

I 



tan G) = — 2 <to — i ^py M x + ^ ¥ 



wl? 
El' 



1 
K73) 



which agree with the principle already enunciated. 

1 si). To dediic ! formula (67), let A, B, C (Fig. 28) be any 
three consecutive points of support of a beam resting on N 
supports. 



STRAINS IN BEAMS. 121 

From the first of equations (73) we may at once write 

PTTT 

M 3 = - 2M 2 j- tan< t >/ + ho'l^, 

and by considering x positive from B to A, and giving the 
proper sign to tan <f> , we write 

Mi = - 2M 2 + -j- tan <£' + \wl?. 

Multiplying these respectively by V and by l> and adding 
them together, we have 

M.J + 2M 2 (I + V) + M 3 Z' = Jw? + lw'l' z , 

which expresses the relation between the bending moments 
for any three consecutive points of support, and is the same 
as formula (67). 

By a similar process we can find an equation expressing 
the relation between the tangents of the angles taken at the 
three points of support. 



APPLICATIONS OF FORMULA (67). 

190. 1st Case. — Beam in a horizontal position, loaded 
uniformly, resting on three points of support, the segments 
being of equal length. 

In this case, we have T = I, w' — w, and 'M 1 and M 3 each 
equal to zero. Substituting these values in eq. (67), we get 

2(2Z)M 2 = i(2wl% 
whence 

M 2 = iwP. 

The bending moment of the section at B is, eq. (57), 

- IV + -g- = M a = IwP, 
whence we get for the reaction at A, 

which is the same value before found. The reaction at C is 



f 



122 CIVIL ENGINEERING. 

the same, and that at B can now be easily determined, from 
the equation, 

Ei + R 2 + R 3 = 2wL 

Knowing all the external forces acting on the beam, the 
bending moment at any section, the shearing strain, etc., can 
be determined. 

191. 2d Case. — Beam in a horizontal position resting on 
four points of support. 

Ordinarily a beam resting on four supports is divided 
into three unequal segments, the extreme or outside ones 
being equal to each other in length, and the middle one 
unequal to either. 

If we suppose this to be the case, represent by A, B, C, and 
D the points of support in the order given. The bending 
moments at A and D are each equal to zero. To find those 
at B and C, take the general formula (67) and apply it first 
to the pair B C and B A, and then to the pair C B and C D, and 
determine the bending moments from the resulting equa- 
tions. Having found them, the reactions are easily found ; 
and knowing all the forces acting on the beam, the bending 
moments, shearing strains, and curve of mean fibre may be 
obtained. 

192. 3d Case. — Beam in a horizontal position resting on 
five points of support, the segments being equal in length. 

When the number of supports is odd, the segments are 
generally equal in length, or if unequal, they are symmetri- 
cally disposed with respect to the middle point. 

If the beam be uniformly loaded, it will only be necessary 
to find the bending moments at the~points of support of either 
half of the beam, as those for corresponding points in the 
other half will be equal to them. 

Suppose the case of five points of support. , U/vCk 

Let A, B, C, D, and E be the points of supp/ort, C being the 
centre one. Represent by I the length of a segment, w the 
weight on a unit of length, M 2 , M 3 , M 4 , the bending moments 
at B, C, and D, and the forces of reaction at A, B, and C, by 
R b E 2 , R 3 respectively. From the conditions of the problem, 
M 2 is equal to M,, and the reactions at A and B are equal to 
the reactions respectively at E and D. 



STKAINS IN BEAMS. 123 

Applying formula (67) to the first pair of segments, we have 

4ZM 2 -f- ZM 3 = iwl% 

and applying it to the second pair, BC and CD, we get 

M 2 + 4M 3 + IK, = \wl\ 

In these equations, making M 4 equal to M 2 and combining 
the equations, we find 



M 2 = aV^ and ^3 = Tra- 
ces acting on the first segn 
m at B, are — Ri and wL 



The external forces acting on the first segment, AB, to turn 
it around the section at B, are — Ri and wL Hence we have 



whence 

The external forces acting to turn the segment A C or half 
the beam around C are the reactions at A and B and the loads 
on the two segments A B and B C. 

The algebraic sum of the moments for the section at C is, 

- Rfil - EgZ + %wV + \wl? = M 3 = ^wl\ 

Substituting in this the value just found for R x and solving 
with respect to Ita, we get 

R 2 = | fu>l 

The sum of the reactions is equal to the algebraic sum of 
the applied forces, hence, 

E x + R 2 + Kg + R 4 + R 5 = 2R X 4- 2R 2 + R 3 = ±wl, 

in which substituting for Ri and Rg, their values, we find 

R 3 = ftwl. 

The external forces acting on the beam are now all known, 
and hence the bending moments, shearing strain, etc., may be 
determined. 

193. 4th Case. — Beam in a horizontal position, resting on 
n points of support, the segments being equal in length. 

If the beam be uniformly loaded, it will, as in the last case, 
only be necessary to find the bending moments at the points 
of support of either half of the beam. 



124 CIVIL ENGINEERING. 

If n be even, the reaction of the |-^ th and (-§-n + l) th support 
will be equal; if n be odd, the i(n + l) will be the middle 
support, and the reactions of the supports equidistant from the ' 
middle point will be equal. L^ t**Jd-t»*^ (■ 

The formula for the segments would become, n being even, v 

4M 2 + M 3 = iwP, ^ 

M 2 + 4M 3 + M 4 = iwl 2 , 
******** 

In the last equation, ~M i?l + t and M in + 2 would be equal 
respectively to M in _vand Mi».f . j 

From these equations, E 1? E 2 , E 3 , . . . E ra could be obtained. 

GENERAL EXAMPLE. 

194. 5th Case. — Beam in a horizontal position resting on 
n + 1 points of support, segments unequal in length, and 
uniform load on unit of length being different for each seg- 
ment. 

Eepresent the points of support by A x A 2 A 3 . . . k n A n + u 
and the respective bending moments at these points of 
support by M l5 M 2 , M 3 , .... M n , M n + ± . Eepresent the 

length of the segments by l u l 2 , l 9 l n and the respective 

units of weight on the segments by w^ w 2 , w 3 , . . . . w n . 

The bending moments M 1? M n + t being those at the ex- 
tremities, are each equal to zero, and therefore there are only 
n— 1 unknown moments to determine. Applying eq. (67) suc- 
cessively to each pair of segments, we obtain n — 1 equations 
of the first degree with respect to these quantities, which 
by successive eliminations give us the values of the moments, 
M 5 , M s) M„. 

These equations will be of the following form : 

2 (4 + y M 2 + Z 2 M 3 = | (wA 3 + wj*) 
Z 3 M 2 + 2 (l 2 + l t ) M, + Z 3 M 4 = i (wj: + w s l*) 
******** 
4-1 M n _x + 2 (4-i + 4) M, 4 = J (^_x ^.fw, Z 8 *). 

From these equations, the reactions at the points of sup- 
port can be determined, and knowing all the external forces, 
the strains on the beam may be calculated. 



\\ 



TORSION. 



TORSION. 



195. In fig. 9, if the plane C D rotates around some axis 
perpendicular to its plane, the section A B, being fixed, the 
fibres are said to be subjected to a strain of torsion. 

Whenever a beam has one of its ends fixed (Fig. 30), and 
is acted upon by a system of forces among which is a couple 
acting in a plane perpendicular to the axis of the beam, a 
strain of torsion on the fibres of the beam follows. 



D 

Fig. 30. 




Fig. 31. 



The couple acting in the plane of cross- section tends to 
turn this plane about some axis perpendicular to it, and to 
twist the fibres of the beam from their straight directions 
into lines which are helices. 

Let C D be any cross-section of the beam at a distance x 
from the free end, and suppose the applied forces acting in 
the plane of the end section at F. The twisting action pro- 
duced by the moment of the couple at F is transmitted from 
section to section until it reaches C D. In the section, 
C D, supposing it to be fixed, the resistances will act as a 
couple whose moment will be directly opposed to the mo- 
ment of the couple at F. 

Represent by a the angle made after twisting, by two lines 
drawn through the centres of the cross-sections at C D and at 
F ; which lines were in the same meridian plane before the 
twisting force was applied. This angle is assumed to vary, 
directly with the distance between the sections. Represent 
by /3 the angular change for a unit of length. 

Assume as the pole, Z as the fixed line, r and v the co- 
ordinates, of a system of polar co-ordinates in the plane of 
cross-section, C D. (Fig. 31.) 

Any elementary area, as a, of this section is 



r dr civ. 



126 CIVIL ENGINEERING. 

The resistance offered by this elementary area is by hypo- 
thesis directly proportional to its area ; to the angular change, 
/3 ; and to its distance, r, from the axis of rotation. 

The resistance of this area will be, from these hypotheses, 

a x r/3G', or r*drBckr x G', 

in which G' is a constant depending upon the material and is 
to be determined by experiment. 

This resistance acts perpendicularly to r, and its moment 
with respect to the axis through is 

G' /3 r 3 dr dv. 

The total moment of the resistances will be 



t = Q'pf fr^drdv. . . . (74) 



Represent the moment of the couple acting at F by F' x X, 
and we have 



G'/3 f fr*drdv = 'F% . . . (75) 



in which X is the lever arm. 

This expression / / r s dr dv is called the polar moment 

of inertia ; that is, the moment of inertia of a cross-section 
of the beam about an axis through its centre and perpendicu- 
lar to the plane of cross-section. 

Representing it by I p and supposing the plane in which 
the resistance is considered is at the distance I from the 

applied force, we have, since j3 = — , 

G^I, = F'\ (76) 

If the cross-section is a circle, we have I p = i?rr' 4 , r' be- 
ing the radius of the circle. Substituting and solving with 
respect to G', we have 

G ' = ^ X a' ■ • • • W 
from which the value of G' may be found. 



TORSION. 127 



VALUES OF G . 

196. General Morin, in his work on strength of materials, 
gives the values for G' for different materials. 
The following are some of the values : 

Wrought iron G' = 8,533,700 lbs. 

Cast-iron G' = 2,845,000 lbs. 

Cast-steel G' = 14,223,000 lbs. 

Copper G' = 6,210,000 lbs. 

Oak G' = 569,000 lbs. 

Pine G' = 616,000 lbs. 



RUPTURE BY TWISTING. 

197. It is assumed that the strain upon any fibre of the 
beam varies directly with its distance from the axis of tor- 
sion ; and that the sum of the moments of the resistances of 
the fibres is equal to the sum of the moments of the twisting 

Represent by T the modulus of torsion, or the strain" on 
the unit of cross-section where the fibres begin to tear apart 
under the action of the force of torsion. From the hypothe- 
sis, this unit will be the one farthest distant from the axis of 
torsion. 

Use the notation of the last article for the other quantities, 
and we have 

TV dr dv = the twisting stram on the fibre farthest dis- 
tant from the axis of torsion. 

Represent by d the distance of this fibre from this axis, and 
we have 

T 

-rr dr dv — the twisting* o fcrain on the fibre which is at a 
a & 

unit's distance from the axis of torsion. This expression mul- 
tiplied by r gives the twisting s t rain* - on any fibre of the 
beam ; and multiplying this product by r will give the mo- 
ment of resistance of any fibre to torsion, or 

T 

-, r 3 dr dv. 
d 

Hence, we have 

jffr*drdv = ¥'\, .... (78) 









128 CIVIL ENGINEERING. 

or 

Solving with respect to T and we have 

T' = F\x^, . . . . (79) 

from which the values of T may be found. 

Substituting for d and I p , their values where the cross- 
section is a circle, and we get 



INFLUENCE OF TEMPERATURE. 

198. The influence of changes in temperature, especially 
in the metals, forms an important element to be considered 
in determining the amount of strain on a beam. 

If the beam is free to move at both ends, there will be no 
strain in the beam arising from the changes of temperature ; 
if the ends are fixed, there will be, and these strains must be 
determined. 

The elongation or contraction produced by the changes of 
temperature is known for the different metals. The amount 
of strain upon the unit of area will be the same as that pro- 
duced by a force elongating or contracting the beam an 
amount equal to that resulting from the change of tempera- 
ture under consideration. 



CHAPTEK TIL 

STRENGTH OF BEAMS. 

PROBLEMS. 



199. The object of the previous discussions has been to find 
the strains to which a beam is subjected by certain known 
forces applied to it. 

The problems which now follow are : 

Knowing all the external forces acting on a oeam, to de- 
termine the form and dimensions of its cross-section, so that 



STRENGTH OF BEAMS. 120 

the strain on the unit of surf ace shall at no point be greater 
than the limit allowed ; and knowing the form and dimew- 
sions of the cross-section of a beam, to determine the load 
which it will safely bear. 

There are two cases ; one is where the cross- section is con- 
stant throughout the beam ; and the other is where it varies 
from one point to another. 
' . 
1st Case.-^-Beams of Uniform Cross-section. 

200. Strength of beam strained by a tensile force. 

Let AY be the resultant force whose line of direction is in 
the axis of the beam and whose action is to elongate it. 
From the equation preceding eq. (5), we have 

W 

— - = the slsraki on a unit of cross-section. 
A 

Knowing the value of T for different materials, a value less 

than T for the given material is assumed for the &fe*ain to be 

allowed on the unit of cross-section. Assuming this value of 

the steam- and calling it T x , we have 

W 

A = Yi '(80) 

From which, knowing the form of cross-section and its area, 
the problem can be solved. 

Suppose the form to be rectangular, and let b be the 
breadth and d the depth. Then 

W 
A = b x d, or bd = — ; 
J-i 

in which, if b be assumed, d can be determined, and the con- 
verse. 

The solution of the reverse problem is evident. Knowing 
A and T l5 the value of W, or the load which will not produce 
a strain greater than T x on the unit of area, is easily deter- 
mined. 

201. Strength -when strained by a compressive force. 

For all practical purposes, it is assumed sufficiently exact 
for short pieces to apply the methods just given for tension, 
substituting C x for T t ; the former being the assumed limit of 
compressive iM i»ain on the unit of area. When the pieces are 
longer than five times their diameter, they bend under the 
crushing load and break by bending, or by bending and 
by crushing. 
9 



130 



CIVIL ENGINEEEING. 



Rankine gives the following limits of proportion between 
length and diameter, within which failure by crushing alone 
will take place, and be von d which there is a sensible ten- 
dency to give way by bending sideways. 

Pillars, rods, and struts of cast iron, in which the length 
is not more than live times the diameter. 

The same of wrought iron, not more than ten times the 
diameter. 

The same of dry timber, not more than twenty times the 
diameter. 

202. Formulas for obtaining the strength of columns 
or pillars whose lengths are greater than five times the 
diameter of cross-section, and subjected to a compressive 
strain. 

The formulas deduced by Mr. Hodgkinson, from a long series 
of experiments made upon pillars of wood, wrought iron, and 
cast iron are much used in calculating the strength of pillars 
or columns strained by a force of compression. 

Hodgkinson's Formulas. 

Table for finding the strength of pillars, in which 
W = the breaking weight, in tons of 2,000 pounds ; 
L z= the length of the column in feet ; 
D = the diameter of exterior in inches ; 
d = the diameter of interior in inches. 



Nature of column. 



Both ends being round- 
ed, length of column 
exceeding 15 times 
its diameter. 



Both ends being flat, 
the length of column 
exceeding 30 times 
its diameter. 



Solid square pillar of 
red cedar (dry). . , 

Same of oak (Dantzic) 
dry 



W 



8.7 



L^ 



D* 



w =.12.25 



Solid cylindrical col. of 
wrought iron .... 



W = 47.9 



D3-76 



W = 149.7 



D 3-65 



SoM cylindrical col. of 
cast iron 



w = ie.e££ 



Hollow cylindrical col. 
of cast iron 



W = 14.5 



L 



W = 49.4^ 



L»-* 



W = 49.G 



L 1 

D 3> " d'- 6t 



STRENGTH OF PILLAES. 



131 



If the column he shorter than that given in the table, and 
more than five times its diameter, the strength may be deter- 
mined by the following formula : 



W = 



W'AO 



W'+fAC 



(81) 



in which W'= the breaking weight, computed from the 
formulas in the above table ; 

C = the modulus of crushing in tons ; 

A — the cross-section in square inches ; and 

W = the strength of the column in tons. 



Gordon's Formulas. 

These are deduced from the same experiments, and are as 
follows : 

Solid Pillars. 



Cross-section a square. 

Of cast iron . . . . W 



Of wrought iron 



80,000 A 



1 + 



f 



266 tf 
36,000 A 



1 + 



& 



,000 ¥ J 



(82) 



Hollow Pillars. 
Circular in cross-section. 



Of cast iron . 



Of wrought iron 



. . W = 



80,000 A 1 



1 + 



w = 



400 d 2 
36.000 A 



1 + 



3 ; 000 a? , 



(83) 



132 



CIVIL ENGINEERING. 



Cross-section a square. 
Of cast iron . . . 



Of wrought iron 



w _ 80,000 A 
+ 533 & 



W = 



36,000 A 



1 + 



6,000 V 



(84) 



in which, 

W = the breaking load in pounds ; 
A — the area of cross-section in square inches ; 
I = the length of the pillar in inches ; v*- l 

b — the length of one side of the cross-section^; and 
d = the diameter of the outer circumference of the base, v-w 
These formulas apply to pillars with flat ends, the ends 
being secured so that they cannot move laterally and the load 
uniformly distributed over the end surface. In the hollow 
columns, the thickness of the metal must not exceed -§- of the 
outer diameter, j^-vw ^ J ^Ttw, d*. » 

Mr. C. Shaler Smith's Formula. 



This formula is deduced from experiments made by Mr. 
Smith on pillars of both white and yellow pine, and is 

5,000 
.004 I S .... (85) 



W 



in which b and I are in inches, and the same quantities as in 
the preceding formulas. W is the breaking load on the 
square inch of cross-section. v%v |via^ V--* 

203. Mr. Hodgkinson, in summing up his conclusions de- 
rived from the experiments made by him on the strength of 
pillars, stated that : 

" 1st. In all long pillars of the same dimensions, the resist- 
ance to crushing by flexure is about three times greater when 
the ends of the pillars are flat than when they are rounded. 

" 2d. The strength of a pillar, with one end rounded and 
the other flat, is the arithmetical mean between that of a 
pillar of the same dimensions with both ends round, and one 
with both ends flat. Thus of three cylindrical pillars, all of 
the same length and diameter, the first having both its ends 



STRENGTH OF TILLAE5. 133 

rounded, the second with one end rounded and one flat, and 
the third with both ends flat, the strengths are as 1, 2, 3, 
nearly. 

" 3d. A long, uniform, cast-iron pillar, with its ends firmly 
fixed, whether by means of disks or otherwise, has the same 
power to resist breaking as a pillar of the same diameter, and 
half the length, with the ends rounded or turned so that the 
force would pass through the axis. 

" 4th. The experiments show that some additional strength 
is given to a pillar by enlarging its diameter in the middle ■ 

part ; this increase does not, however, appear to be more than , 
one-seventh or one-eighth of the breaking weight." 

Similar pillars. — " In similar pillars, or those whose length 
is to the diameter in a constant proportion, the strength is 
nearly as the square of the diameter, or of any other linear 
dimension ; or, in other words, the strength is nearly as the 
area of the transverse section. 

" In hollow pillars, of greater diameter at one end than the 
other, or in the middle than at the ends, it was not found that 
any additional strength was obtained over that of cylindrical A 

pillars. 

" The strength of a pillar, in the form of the connecting 
rod of a steam-engine " (that is, the transverse section pre- 
senting the figure of a cross +), "was found to be very 
small, perhaps not half the strength that the same metal 
would have given if cast in the form of a uniform hollow 
cylinder. 

" A pillar irregularly fixed, so that the pressure would be 
in the direction of the diagonal, is reduced to one-third of its 
strength. Pillars fixed at one end and movable at the other, 
as in those flat at one end and rounded at the other, break at 
one-third the length from the movable end ; therefore, to 
economize the metal, they should be rendered stronger there 
than in other parts. 

" Of rectangular pillars of timber, it was proved experimen- 
tally that the pillar of greatest strength of the same material 
is a square." 

Long-continued pressure on pillars. — " To determine 
the effect, of a load lying constantly on a pillar, Mr. Fairbairn 
had, at the writer's suggestion, four pillars cast, all of the 
same length and diameter. The first was loaded with 4 cwt., 
the second with 7 cwt., the third with 10 cwt., and the fourth 
with 13 cwt. ; this last load was y^ of what had previously 
broken a pillar of the same dimensions, when the weight was 
carefully laid on without loss of time. The pillar loaded 



134 CIVIL ENGINEERING. 

with 13 cwt. bore the weight between five and six months, 
and then broke." 



STRENGTH OF BEAM TO RESIST A SHEARING FORCE. 

204. It has been shown that the transverse shearing strain 
varies directly with the area of cross-section, and that we have 

S' = AS, 

in which S is the modulus of shearing. Assuming a value 
which we represent by S x less than S for the given material, 
and we have 

in which W is the force producing shearing stain and Si the 3 
limit of the shearing strain allowed on the unit of surface. 

n,Ajthe din 
the cross-section are easily obtained. I v j*7 I -, 



Knowing the form of cross-section,Athe dimensions to give 

TRANSVERSE STRENGTH OF BEAMS. 

205. The stress on the unit of area of the fibres of a beam 
at the distance y from the neutral axis, in the case of trans- 
verse strain, is obtained from eq. (21), 

* 

As ^previously stated, the hypothesis is that the strain on 
the unit of area increases as y increases, and will be greatest 
for any section when y has its greatest value. That unit of 
area in the section farthest from the neutral axis will there- 
fore be the one that has the greatest strain upon it. Now 
suppose A^Vio be increased gradually and continually. It 
will at length become so great as to overcome the resistance 
of the fibres and to produce rupture. Since the material is 
homogeneous, and supposed to resist equally well both ten- 
sion and compression, the strains on the unit of area at the 
same distance on opposite sides of the neutral surface are 
considered equal. 

Representing by R the stress on the unit of area farthest 
from the neutral surface in the section where rupture takes 
place, we may write 

7=fe'£. • • • • (86) 
in which W^Js the &w»ee necessary to produce rupture. 



TIIANSVEESE STRENGTH OF BEAMS. 135 

When the cross-section i$ a rectangle, in which b is the 
breadth and d the depth, I is equal to T V^ 3 ? and the greatest 

d 

value of y is - ; substituting these values in eq. (86) we have 

for a beam with rectangular cross-section, 



E x $d 2 =(w'x.) .... (87) 



The first member is called the moment of rupture and 
its value for different materials has been determined by ex- 
periment. 

These experiments have been made by taking beams of 
known dimensions, resting on two points of support, and 
breaking them by placing weights at the middle point. 

From equation (87) we have 

R ~w (88) 

in which, substituting the known quantities from the exper- 
iment, the value of K, called the modulus of rupture, is 
obtained. 

These values, thus obtained, are especially applicable to all 
beams with a rectangular cross-section, and with sections that 
do not differ materially from a rectangle. "Where other 
cross sections are used, special experiments must be made. 

, 206. In a beam of uniform cross-section the strains on the 
different sections vary, and that particular section at which 
the moment of the external forces is the greatest is the one 
where rupture begins, if the beam break. This section most 
liable to break may be called the dangerous section. 

In rectangular beams the dangerous section will be where 
the moments of the straining forces are the greatest. 

Let W denote the total load on a beam, and I its length, we 
have for the greatest moments in the following cases : 

M =Wl, when the load is placed at one end of a beam, and 
the other end fixed. 

M=— x I = £Wl, for the same beam uniformly loaded. 

W I 
M = — x -k~ JWZ, when the load is placed at the middle 

point of a beam resting its extremities on supports. 

M — — X iy = $Wl, for the same beam uniformly loaded. 

If a less value than that necessary to break the beam be 



136 CIVIL ENGINEERING. 

substituted in eq. (88) for (Wiy the corresponding value for 
E, will not be that for the modulus of rupture, but will 
merely be the strain on the unit of area farthest from the 
neutral axis in the section whpse v abscissa is x. Let W'be -» 
-J^c^es^tkaffl-W^pattd give to^ciits values corresponding to 
the maximum moments. Substituting these in eq. (87), we 
have 

R'xJ$tf=iWZ.j (89) 

■R'xpd 2 =Wl. 

in which E' is the maximum strain on the unit of area in 
the dangerous section for the corresponding cases of rectan- 
gular beams, whose maximum moments are given above. 

These formulas show the relations existing between E', W, i * 
b, and d for rectangular beams under the given circumstances, 
and enable us, knowing feee of the quantities, to deduce the 

Thus knowing W r f>, and d, we find the value of E', by 
substituting their values in the formula and solving with 
respect to R/. w 

In the same way knowingJV and E', or assuming values for 
them, we substitute them in the formula, and deduce an ex- 
pression containing b and d, in which by giving a value to b 
or d, the other may be deduced, and the two taken together 
give the cross-section which the beam must have in order that 
for the given weight, the greatest strain should be equal to the 
assumed one that h i m beun substituted fur R'. , 

Knowing E for the given material, b and d, we find "Writhe 



. /' breaking waigkfc, from eq. (88) 
207. From the definiti 



207. From the definition for E, it would seem, as before 
stated, that it should be equal either to T or to C, depending 
upon whether the beam broke by crushing or tearing of the 
fibres. In fact, it is equal to neither, being generally greater 
than the smaller and less than the greater ; as shown in the 
case for cast iron, for which 

The mean value of C = 96,000 pounds ; 
The mean value of T = 16,000 pounds ; and 
The mean value of E = 36,000 pounds. 

If, then, instead of taking R from the tables, the value of T 
or C be used, taking the smaller value of the two, the calcu- 
lated strength of the beam will be on the safe tide. That is, 






INFLUENCE OF CROSS- SECTION. 137 

the strength of the beam will be greater than that found by 
calculation. 

Experiments should be made upon the materials to be used 
ill any important structure, to find the proper value for R. 

In determining the safe load to be placed on a beam, the 
following values for R ; may be taken as a fair average : 

For seasoned timber, R' = 850 to 1,200 pounds ; 

For cast iron, R' = 6,000 to 8,000 pounds ; 

For wrought iron, R' = 10,000 to 15,000 pounds. 



INFLUENCE OF THE FORM OF CROSS-SECTION ON THE STRENGTE 

OF BEAMS. 

208. The resistance to shearing and tensile strains in any 
section of a beam is the same for each unit of surface through- 
out the section. The same has been assumed for the resist- 
ance to compressive strains within certain limits. Hence so 
long as the area of cross-section contains the same number of 
superficial units, the form has no influence on the resistance 
offered to these strains. 

This is different in the case of a transverse strain. 

We may write equation (21) under this form, 



to. 



In this, if we suppose Wod to have a constant value, P will then 

y 

vary dirfectly with the factor — ; that is, as this factor increases 

or decreases, there will be a corresponding increase or decrease 
in P. 

Represent by d the depth of the beam, \d will be the 
greatest value that y can have. It is readily seen, that for 
any increase of %d, I will increase in such a proportion as to 

decrease the value of -y, and hence decrease the amount of 

strain on the unit of area farthest from the neutral axis. 
Therefore we conclude that for two sections having the same 
area, the strain on the unit of surface farthest from the neutral 

axis is less for the one in which ^ is the greater. 

This principle affords a means of comparing the relative 
resistances offered to a transverse strain by beams whose cross- 
sections are different in form but equivalent in area. 






138 CIVIL ENGINEERING. 

For example, compare the resistances offered to a trans- 
verse strain by rectangular, elliptical, and I-girders, with 
equivalent cross-sections. 

The values of I for the rectangle, ellipse, and I-section are 
respectively, 

1 = T i_^ 3 , 1 = -fairbcP, and I = T \{hd 3 - I'd'*). 

.Represent the equivalent cross-section by A, and we will 
have A = hd for the rectangle, A = \irbd for the ellipse, and 
A = h(d—d') for the I-section. The latter is obtained by 
neglecting the breadth of the rib joining the two flanges, its 
area being small compared with the total area, a n d- b y ™ ?. 
ryV>, ing d 2 = ddf = d' 2 , d — d' being small compared with d. 

Substituting these values of A in the factor ■—, and we get 

6 8 2 

for the rectangle, — - ; for the ellipse,-— ; for the I-section — . 

J\-W £^.Ct £$*.(& 

Hence we see that ^=r is least for the third, and greatest for 

the second, and therefore conclude that the strain on the 
unit of surface farthest from the neutral axis is the least for 
the I-girder, and its resistance to a transverse strain is greater 
than either of the other two forms. 

Since the quantity A. contains h and d, by decreasing b and 
increasing d, within limits, the resistance of any particular 
form will be increased. And hence, in general, the mass of 
fibres should be thrown as far from the neutral axis as the 
limits of practice will allow. * 

The strongest Beam that can be out out of a Cylin- 
drical Piece. 

209. It is oftentimes required to cut a rectangular beam 
out of a piece of round timber. The problem is to obtain the 
one of greatest strength. 

Denote by D the" diameter of the log, by b the breadth, 
and 'd the depth of the required beam. 

From the value r 

R ;J&<*> 

u - iw 

it is evident that the strongest beam is the one in which M 2 
has its maximum value. 



BEAMS OF UNIFORM STRENGTH. 139 

Representing the cross-section of the beam and of the log 
by a rectangle inscribed in a circle, we have 

D being the diameter of the circle. Multiplying by h, gives 

hk = bD 2 -h\ 

In order to have bcP a maximum, D 2 — 3h 2 must be equal to 
zero, which gives 

and this, substituted in the expression for d 2 , gives 

d = DVl. 

To construct this value of 5, draw a diameter of the circle, 
and from either extremity lay off a distance equal to one- 
third of its length. At this point erect a perpendicular to 
the diameter, and from the point where it intersects the cir- 
cumference draw the chords joining it with the ends of the 
diameter. These chords will be the sides of the rectangle. 

2d Case.-^vBeams of Yariable Cross-section. 

210. Beams of uniform strength. — Beams which vary 
in size so that the maximum strain on the unit of area in each 
section shall be constant throughout the beam form the prin- 
cipal class of this second case. 

In the previous discussions and problems the bar or beam 
has, with but one exception, been considered as having a 
uniform cross-section throughout, and in these discussions the 
moment of inertia, I, has been treated as a constant quantity. 

Since the beams had a uniform cross-section it is evident 
that the greatest strain on the beam was where the moment 
of the external forces was the greatest. 

Finding this maximum moment of the external forces, we 
determined the maximum strains and the s'ection at which it 
acted. If this section was strong enough to resist this action, 
it follows that all other sections were strained less and were 
larger than was necessary to resist the strains to which they 
were exposed ; in other words, there was a waste of material. 

The greatest strain on a unit of surface of cross-section 
being known or assumed, let us impose the condition that it 
shall be the same for every section of the beam. This will 



*L> 



140 CIVIL ENGINEERING. 

necessitate variations in the cross-sections, hence I will vary 
— and must be determined for each particular case. 

A beam is call a " solid of equal resistance " when so 
proportioned that, acted on by a given system of external 
forces, the greatest strains on the unit of area are equal for 
every section. 

This subject was partly discussed under the head of tension 
in determining the form of a bar of uniform strength to resist 
elongation. The method there used could be applied to the 
case of a beam to resist compression. 

Beams of Uniform Strength to resist a Transverse 

Strain. 

211. Suppose the beam to be acted upon by a force produc- 
ing a transverse strain, and let the cross-section be rectangular. 

Let h and d represent the breadth and depth of the beam, 
and we have 

I = ^U\ 

Substituting in eq. (21) this value Of I, and giving to y its 
greatest value, which is ^d, we have 

P' x fid? =(Wx, 
or r 






Wx 



^w- 



"6 



(90) 



for the stress on a unit of surface at the distance \d from the 



neutral axis in the cross-section w h o oe/abacissa 

For any assumed constant value for (\\Jythe greatest strain 
will be found in that section for which x has its maximum 
value. Let x — I be this value, and represent by P" the 
value of P', for this value of x, and we have 

P"-^ (91) 

~m (91) 

This value of P" is then the maximum value of the stress, 
upon the unit of surface, produced by the deflecting 
force, yf. 

From the conditions of the problem, the greatest strain on 
the unit of surface must be the same for every cross-section. 
Eq. (90) gives the greatest strain on the unit of surface in any 
cross-section. It therefore follows that for a rectangular beam 
of uniform strength to resist a cross strain, we must have 

p--I^> m 

1 -{/hP ( '-> 



BEAMS OF UNIFORM STRENGTH. 



Ill 



Since P" is constant, b or d, or both of them, must vary as 
x varies, to make the equation a true one; that is, the area of 
cross-section must vary as x varies. 

"We may assume b constant for a given case, and giving 
different values to x, deduce the corresponding ones for d; 
or, assuming d constant, do the same for b ; or we may assume 
that their ratio shall be constant. 

For the first case, b, the breadth constant, we have 

For the second case, <:Z, the depth constant, we have 



<0 My) ) 



b = 



CWa?J 

fP"d 2 > 



(94) 



and for the third, their ratio constant, b = rd, we have 



i * 



CL - 






d" 



(95) 



The assumed values of x with the deduced values of d, 
from eq. (93), will show the kind of line cut out of the beam 
by a vertical section through the axis, when the breadth is 
constant ; and the deduced values of b, from eq. (94), will 
show the kind of line cut out of the beam by a horizontal 
section through the axis when the depth is constant. These 
lines will show the law by which the sections vary from one 
point to another throughout the beam. 

As examples take the following cases : 

212. Case 1st. — A beam firmly fastened at one end 
(Fig. 32), its breadth constant, and the other end free to 




Fig. 32. 



move strained by a load uniformly distributed along the 
line, A B. 



142 



CIVIL ENGINEERING. 



Take B as the origin of co-ordinates, B A the axis of X, y 
positive downwards, the axis of Z horizontal, and w the weight 
on a nnit of length. 

The moment of the weight acting at any section as M is 

—^r 1 substituting which for Wx in the expression (93) for d, 
we have ^ 

d = y=±x\Jpr b ,"± ^' I 

which is the equation of a right line as B D, passing through 
the origin of co-ordinates. 

If the depth be constant, the breadth will vary from point 
to point, and the different values of the ordinate may be ob- 
tained by substituting this moment for Wx in expression (94), 
and we have 

Sw 
o — z 



*£ I 



which is the equation of a parabola having its vertex at B, 
as in Eig. 33. 




Fig. 33. 



213. Case 2d. — A beam as in preceding ease strained 
by a load, W, concentrated and acting at B, the weight 
of the beam disregarded. 

The breadth being constant, we have 



d 



y 



= ± i/g^fc^ 



or 



f 



6W 



1 £ 



•'.' t 



BEAMS OF UNIFORM STRENGTH. 



143 



which is the equation of a parabola, the vertex of which is 



at B. Fig. 34. 




Fig. 34. 



Suppose the depth constant ; in this case we have 



s = 



6W 



-h 



* 



which is the equation of a right line, and shows that the plan 
of the beam is triangular. 

214. Case 3d. — Suppose tlie beam resting on two sup- 
ports at its ends and uniformly loaded. 

Represent by 2Z the distance between the supports, by w 
the load on a unit of length, and take C (Fig. 22) as the origin 
of co-ordinates. 

The moment of the external forces at any section at the 
distance (Z — x) from B will be — \w{p — x 2 ) which substi- 
tuted in eq. (93), gives 

3^ 3rf 

which is the equation of an ellipse. 

This moment substituted in eq. (94), gives 



b = 



Sw 



v? 



3wP 



which is the equation of a parabola. 

215. In a similar way we may determine the forms of beams 
of rectangular cross-section, when other conditions are im- 
posed. 

If we had supposed the sections circular, then I = ^7rr 4 , 
and this being substituted for I in the general expression for 



. 144 CIVIL ENGINEERrNG. 

the steam, on a unit of surface farthest from the neutral axis, 
a similar process would enable us to determine the form of 
the beam. 

Hence, knowing the strains to which any piece of a structure 
is to be subjected, we may determine its form and dimensions 
such that with the least amount of material it will successfully 
resist these strains. 



DELATION BETWEEN STRALN AND DEFLECTION PRODUCED BY A 
BENDING FORCE. 

216. Within the elastic limit, the relation between the 
greatest strain on the fibres and the maximum deflection of 
the beam produced by a bending force, may be easily deter- 
mined. 

Take a rectangular beam, supported at the ends and loaded 
at its middle point. 

The third of equations (89) gives for this case 

K' x ibd 2 = JWZ, 
and solving with respect to "W, we have 

W-,™ 
W ~ 3 I ' 

in which W is the load on the middle point of the beam. 

The maximum deflection produced by the load, W, in this 
case has been found to be 

Substituting for I its value for a rectangle, we have 

J ~ t E W 

Solving with respect to W, and placing it equal to the value 
of "W obtained from eq. (89), we have 



from which we get 



^i-dff, 



CE<Z 



E' = ^-/ (96) 



OBLIQUE FORCES. 



145 



Hence, knowing the deflection and the coefficient of elasti- 
city, the maxium strain of the fibres can be obtained and the 
converse. 



FORCES ACTING OBLIQUELY. 

217. The forces acting on the beam have been supposed to 
be in the plane of, and perpendicular to, the mean fibre. 

The formulas deduced for this supposition are equally 
applicable if the forces act obliquely to the mean fibre. 

Suppose a force acting obliquely in the plane of the mean 
fibre, it can be resolved into two components, one, P, perpen- 
dicular, and the other, Q, parallel to the fibre. The com- 
ponent P will produce deflection, and the component Q, 
extension or compression depending on the angle, whether 
obtuse or acute, made by the force with the fibre. 

The strains caused by each of the components can be deter- 
mined as in previous cases. 

For suppose the force applied in the plane of the axis of 
the beam, at F (Fig. 35), and let x be the distance to any sec- 
tion, as K, measured on the axis of the beam E F. 




Let 
I 

by the 




Fig. 35. 



Fig. 36. 



= E F, the length of the beam, and a = the angle made 
axis E F with the vertical. 
10 



146 



CIVIL ENGINEERING. 



The bending moment at any section, as K, is equal to 
PxFK, 
or 

Wx sin a. 

The maximum moment will be ~Wl sin a. 

In Fig. 35 the component Q = W cos a tends to compress 

the beam, and in Fig. 36 it tends to elongate it. 

If the beam is rectangular, the stress upon the unit of 

r • • i . W cos a ' 

surface m either case is — 7-5 — , and must be deducted from 



/. 



ta 



B, in determining the strength of the beam. 

Hence at the dangerous section for a rectangular beam, we 
have , 

Wl sin a = * (E - —^y j( p. . (97) 

And in general the condition is imposed ,that the sum of 
the strains on any unit of surface must not be greater than 
that found or assumed for the strain on the unit of surface 
farthest from the neutral axis. That is, 
Px 
I 



Q 
4d + J<K. 



The shearing strain on this unit of surface is caused by the 



force -T-, hence 



<S. 



TWISTING STRENGTH OF BEAMS. 



218. If the force act outside of the plane of symmetry, a 
third component, parallel to the axis of Z, is introduced, tend- 
ing to turn the beam about its axis, and to prod uce a strain of 
torsion if the ends be firmly fastened. This twisting strain 
should never be allowed in any of the parts of a structure. 
But if the strain be necessary its amount on the unit of sur- 
face may be deduced by the use of formulas (76) and (79), 
and the proper dimensions of the beam calculated. 

It is sometimes important to find the force necessary to 
break a given cylinder by twisting. 

The following formula, deduced from experiment, may be 
used, 



W 



(98) 



ROLLING LOADS. 147 

in which T" = the weight in pounds required to break by 
twisting a solid cylinder of the same material, one inch in 
diameter, the weight acting at the distance one inch from 
the axis of the cylinder ; d = the diameter, in inches, of 
the cylinder whose resistance to torsion is desired ; r = the 
distance^ from its axis to the point of application of the applied 
force. ^ C*jU*a*& 

Haying found the value of T" by experiment, and knowing 
d and r, W can be deduced. 

ROLLING LOADS. 

Strength of a beam to resist a moving load. 

219. The action of a stationary load, or forces whose points 
of application are constant during the discussion, have been 
the only kinds of forces considered in the previous examples. 

Many structures are intended to support loads which are 
in motion with respect to the structure ; as a bridge support- 
ing a load which comes on at one end and moves off at the 
other. 

These moving loads are called rolling loads, from the 
manner in which they are placed on the structure, or live 
loads, to distinguish them from those which are stationary or 
fixed. 

220. Let it be required to determine the strains in the 
case of axbeam uniformly loaded, supported at its extre- 
mities, aiiQs acted upon by an additional load which rolls 
on the beam, at one end and off at the other. 

Suppose this rolling load to be uniformly distributed in a 
horizontal direction. 
Represent by (Fig. 37), 

21 — A B, the length of the beam ; 

w = the weight of the uniform stationary load, on the 

unit of length ; 
w' = the weight of the rolling load on the unit of 

length ; 
R x I? 2 , the reactions at the points of support ; 
m, the length of the rolling load in any one position ; 

and 
n = 21 — m, the length of that part of the beam not 
covered by the moving load. 
The reactions at the points of support, due to the uniform 
load on the beam and the live load from A to D, are 

_. 7 . 21 — y _ _ _ , m 

Ki = wl + wm — ^ — , and K 2 = wo -f w m-rj* 




us 



CIVIL ENGINEEEING. 



Take the origin of co-ordinates at A, the axes of X and Y, 
as before, and the reactions negative. 



I 



"* 



c /> 

Fig. 37. 



Moments. — The bending moment at any section whose 
abscissa is x, and which lies between A and D, will be 



M — — K^ + (w + w') 



2' 



(99) 



and for any section between D and B, the abscissa being x, 



M = — K^ + 



wx 2 w'm 



(2a?— m). 



(100) 



It will be seen from these, after substituting for E T its value, 
that the greatest bending moment will be m = 21, or when 
the rolling load extends entirely over the beam. And we 
have 

M=(w+w)(j-lx\ . . . (101) 

for the bending moment at any section when the rolling 
load extends over the entire beam. 

If the beam be made strong enough at the dangerous sec- 
tion to support this load, it will be strong enough to resist 
the cross strain for all other rolling loads, whose weight per 
unit of length does not exceed w'. 

Shearing strain. — The shearing strain at any section be- 
tween A and D, will be 

S' = iw+w') 03-Ei .... (102) 
and for any section between D and B, 

S'=(«w + w'm)-E l . . . . (103) 

Equations (102) and (103) represent two right lines. If we 
give all values to m from zero to 2Z, the right lines can be 
constructed which will represent the shearing strains on the 
sections for the different rolling loads. 



ROLLING LOADS. 149 

If the rolling load extends entirely over the beam, the 
shearing strain on any section will be 

^ = (w+w r ) (x-l) .... (104) 

At first glance it might be supposed that eq. (104) would 
give the maximum shearing strain at any section. It will 
not do so, for we will find sections which have a greater 
shearing strain upon them when the rolling load does not 
cover the entire beam, than when the load does cover it. 

Take eq. (102) and substitute for ~R t its value, we get 

(17) \ 

m-^--x) . . (105) 

and eq. (103), by the same substitution, becomes 

S f =zw(x-l)+w ,9? ^- (106) 

Represent by x r the abscissa of any section between D and B. 
Substituting x' for x in eq. (106) we get 

777 

S" = w(x'-T)+w'-q (107) 

for the shearing strain at this section, when the live loaa ex- 
tends to D. Suppose the load covers the entire beam, the 
shearing strain at this section for this case would be, eq. (104), 

S" = (w+w r ) (x'-l) 

which may be written 

S"= w (x r — I) + w' (x' - Z). . . (108) 

To compare these values of S" under these different circum- 
stances, it will only be necessary to examine the terms 

w' (x f — I) and w'-jj'- 

Suppose m >l and take x'= m, that is, the live load extends 
over more than half the beam, and the section under con- 
sideration is the one at the end of the moving load. 

.Remembering that 21 — m + n, we have 

w (x — i) —w \m ;r — I — -{m — n), and . 

.m 2 w' m 2 
w 



U 2 m + n 



150 CIVIL ENGINEERING. 



But m — n < , hence, it is to be concluded, that the 

m + n 7 

shearing strain, at the section at the end of the moving 
load, when this load covers the greater segment of a beam, 
exceeds the shearing strain in the same section produced by a 
load of the same amount on the unit of length extending 
over the whole beam. 

The first part, w (x — I) of the second member of equation 
(106) represents the shearing strain at any section of the 
beam produced by the uniform stationary load. The part, 

w'-jTy the shearing strain at any section between the end of 

the moving load and support B, produced by the moving 
load. 

Give m all values in succepsion from zero to 21, and the 
m 
corresponding values of w'-tj will be the shearing strains 

produced by the live load at the end section of the load in all 
its positions, from the time the load first rolls on the beam 
until the beam is entirely covered by it. 

These different values may be represented by ordinates, 
and the line traced through their extremities will be a para- 
bola. 

If m and x have simultaneous and equal values, equation 
(106) is that of a parabola whose ordinates will represent the 
shearing strain produced by both loads at the end of the live 
load, the length of the latter being at least equal to the length 
of the beam. If we place the second member equal to zero, 
and solve it with respect to x, we have 

- ^-<-*5[- 1 *>A+|J: • • (109) 

That is, when the live load covers the beam from the origin, 
A, to a point distant equal to the value of x' , that there is no 
shearing strain in the section at the end of the live load. 
This is shown graphically, for at this point the parabola 
represented by eq. (106) cuts the axis of X, or the ordinate 
of the curve representing the shearing strain at this point is 
equal to zero. 

By giving values to w and w' this distance in terms of 21 
may be determined. 

As more of the live load comes upon the beam, the point 
of no shearing moves, going towards the centre. When the 
live load entirely covers the beam the point of no shearing is 






LIMITS OF PRACTICE. 151 



at the centre. As the live load moves off the beam, this 



point follows the load mid di^ppoftr i p op that aidcj find at the ;,'" r '"" 
same distance from the end, that it was found in the begin- 
ning from the other. " '^ 

LIMITS OF PRACTICE. 

221. Until quite recently, comparatively speaking, it was 
the custom of most builders, in planning and erecting a 
structure, to fix the dimensions of its various parts from pre- 
cedent, that is, by copying from structures already built. 

So long as the structure resembled those already existing 
which had stood the test of time, this method served its pur- 
pose. But when circumstances forced the builder to erect 
structures different from any in existence or previously known, 
and to use materials in a way in which they had never before 
been applied, the experience of the past could no longer be 
his guide. Practical sagacity, a most excellent and useful 
qualification, was not sufficient for the emergency. Hence 
arose the necessity that the builder should acquire a thorough 
knowledge of the theory of strains, the strength of materials, 
and their general properties. 

The principal object of "strength of materials" is to de 
termine the strains developed in the different parts of a struc- 
ture, and to ascertain if those strains are within the adopted 
limits. And as a consequent, knowing the strains, to deter- 
mine the forms and dimensions of the different parts, so that 
w r ith the least amount of material they shall successfully re- 
sist these strains. 

The limits adopted vary with the materials and the charac- 
ter of the strain. The essential point is that the limit of 
elasticity of the material should not be passed, even when by 
some unforseen accident the structure is subjected to an un- 
usual strain. The adopted limit to be assigned is easily 
selected if the limit of elasticity be known ; but as the latter 
is obtained with some difficulty, certain limits of practice 
have been adopted. 

In many cases this practice is to assume some known weight 
per square inch as the maximum load on a given material ; as 
sandstone must not bear more than 600 pounds to the square 
inch ; granite, 1,200 pounds, etc. From the varying qualities 
of the same material it is easily seen that this method of 
practice differs but little from a " mere rule of thumb." 

The most usual practice, especially for structures of im- 
portance, as bridges, is to determine the breaking weights or 




152 CIVIL ENGINEERING. 

ultimate strength of the different parts, and take a frac- 
tional part of this strength as the limit to be used. The re- 
ciprocal of this fraction is called the factor of safety. 

A more accurate method would be to calculate the dimen- 
sions of the pieces necessary to resist the strains produced by 
the maximum load, and then enlarge the parts sufficiently to 
give the strength determined by the factor of safety. 

When the structure is one of great importance, actual 
experiments should be made on each kind of material used in 
its construction, so that the values deduced for the ultimate 
strength shall be as nearly correct as possible. 

222. These factors of safety are arbitrarily assumed, being 
generally about as follows : 

Material. Factor of safety. 

Steel and wrought iron 3 

Cast iron 6 

Timber 6 

Stone and brick 8 to 10. 

These are for loads carefully put on the structure. 

If the materials and workmanship were perfect, these factors 
could be materially reduced. 

The work performed by a constant force, W, through a 
given space has been shown to be the same as that performed 
by the action of a force increasing at a uniform rate from 
to 2W through the same space. Hence a force, W, applied 
suddenly to a' beam will produce the same strain on the 
beam as 2W applied gradually. 

A rolling load moving swiftly on a structure approximates 
nearly to the case of a force suddenly applied. 

Hence, for rolling loads, the factors of safety should be 
doubled. 



CURVED BEAMS. 

223. Any beam which is made to take a curvilinear shape 
in the direction of its length is called a curved beam. The 
curve assumed by the mean fibre is usually that of a circular 
or parabolic arc. 

For the purposes of discussing the strains on beams of this 
class, it is supposed that: 

1. The beam lias a uniform cross-section ; 

2. That its cross- section is a plane figure, which if moved 
along the mean fibre of the beam and normal to it, keeping 






CURVED BEAMS. 153 

the centre of gravity of the plane figure on the mean fibre, 
would generate the solid ; and 

3. That the dimensions of the cross-section in the direction 
of the radius of curvature of the mean fibre are very small 
compared with the length of this radius. 

If the beam be intersected by consecutive planes of cross- 
section, the hypotheses adopted for a straight beam subjected 
to a cross strain are assumed as applicable to this case. 

224. General equations. — Suppose the applied forces to 
act in the plane of mean fibre, let it be required to deter- 
mine the relations between the moment of resistance 
at any section and the moment of the external forces 
acting on the beam. 

Let E F (Fig. 38) be a curved beam ; the ends E and F 
baiH^fftfoff'£lfrll(i kurrawiliil pWwy and so arranged that the 
horizontal distance between them shall remain constant. 



/ 
/ 



/ / 
/ / 

// 
Fig. 38. 



Let A B be any cross-section. The external forces acting 
on either side of this section are held in equilibrium by the 
resistances developed in this section. Suppose^ B to be fixed, 
and let CD' be the position assumed by the consecutive 
section under the action of the external forces, on the right 
of A B. The resultant of these external forces may be resolved 
into two components, one normal to the curve of the mean 
fibre at 0, and the other parallel to the tangent to this curve 
at this point. Represent the former by F, the latter by P, 
and by M, the sum of the moments of the external forces 
around the neutral axis in the section A B. 

The fibre ah is elongated by an amount be, proportional to 
its distance from the neutral axis. 



154 CIVIL ENGINEERING. 

The force producing this elongation is 
Ea x bo 

or since ab may be considered equal to 0', 

Ea x be 

0' ' 

in which E is the co-efficient of elasticity and a the area of 
cross-section of the fibre, ah. 

Hence, there obtains to express the conditions of equilibrium, 

Ea x be y , jEa x bo 



00 



^<and^^x50J=M. (110) 



Represent by p and p', the radii of curvature, R 0' and R'O'. 

The triangle, aRb, has its three sides cut by the right line, 
R'C. Hence the product of the segments, R 0", bo, and aR' is 
equal to the product of the three segments, R R', bO', and ac. 

Substituting p for RO',/5- p' for R'R, and p r for aR f , since 
O'b is very small in comparison with p\ and we have 

p x bo x p' — (p — p') x bO r x ac. 
From which we get 



bo p — p' 



(H) 



X £0'.= (-,--| x 50' 



ac pp \p p> 

Since ac differs frdm 0' by an infinitely small quantity, 

be 
the expression obtained for — may be taken as the value of 

r ac J 

be DO 

fwy. Substituting this value for tt^/j in the second of equa- 
tions (110), we get. 

fcx(^--)xJ(ax £o' 2 ) = M. . (Ill) 

This sum, 2 (a x bO' 2 ), is tlie moment of inertia of the 
cross-section taken with respect to the neutral axis passing 
through the centre of gravity of the section. Representing 
this by I, equation (111) may be written 

m (}-~) = M >- • • • ( 112 > 

which is the general equation, showing the relation existing 



CURVED BEAMS. 



loo 



between the moments of resistances of any section and the 
moments of the external forces acting on that section. 

225 Displacement of any point of the curve of mean 
fibre. — Let A B (Fig. 39) be the curve of mean fibre before 
the external forces are applied to the beam. 




FIG - 39 - \^Lrf- 



Take the origin of co-ordinates at the middle point, C, and 
the axes X and Y as shown in the figure. 

Let D be any point whose co-ordinates are x and y, and 
represent by cf> the angle made by the plane of cross-section 
at D with the axis of Y. 

Suppose the external forces applied, and denote by x' and 
y' the co-ordinates of D in its new position, and by </>' the 
new angle made by the plane of cross-section with the axis of 
Y. 

It is supposed that the displacement of the point, D, is . so 
slight that M remains unchanged. 

From the calculus we have 



dz 
P = #' aRd 



d$ n 



in which dz and dz are the lengths of the elementary prism 
before and after the strain measured along the mean fibre. 
Since they differ by an infinitely small quantity from each 
other, by making dz = dz' and substituting in equation (112) 



we get 



-Pi 



d(f> 



)= 



M. 



Integrating we obtain 



*-*-/ 



M 
EI 



dz + C. 



(113) 



156 CIVIL ENGINEERING. * 

The component force, parallel to the tangent at D, acts in 
the direction of the length of the fibre. Since the points E 
and F are fixed, this force produces a strain of compression 
on the fibre. The length of this fibre, after compression 
between the two consecutive planes, is represented by dz ', 
and is 

&, = *-Ei = *( 1 - L i5)- 

The values of cos </>, sin <£, cos $', and sin cj>' may be written 
as follows : 

dx . ' dy 

,, dx' . ,, dy' 

Substituting, in the last two of these, the value just found 
for dz', we get 









cos 4> r = ^^-^ , and sin <£' = —^ — -p- 



If ($>' — is very small, we may write 

cos <f>' = cos <f) — ((f)' — <j}) sin (/>, and 

sin ft — sin <£ + (<£' — <jj) cos <£. 

Substituting these values of cos j>' and sin <//, in the expres- 
sions above, and solving with respect to dx' and dy', we get 

dx' = dz\ 1 — p-r- ) (cos $ — (<£' — <j>) sin <£), 

dy' = dzil — y-rj (sin <j> + (<j>' — </>) cos 0). 

Substituting in these for sin <f> and cos <£, their values in 
terms of dz, dy, and dx, we get 

,/, = dx{i - |y - (f - *> «*/ Ir-ffi) 

dy' = d>j{\ - WK )+ W - 4>) dx,r i _ 



CURVED BEAMS. 157 

whence *. , 

P / l JL \ 

dx' - dx = - Yj^dx- ($' - 0) dy,{J - 

dy r -dy=-^ k dy + (f - <f>)dx. ( I -£ ) 



u * A/ 



Integrating, there obtains 
x' — x 



The constants of integration reduce to zero for both equa- 
tions, since from hypothesis there is no displacement of the. 
points at the ends of the curve of mean fibre. 

If the beam is metal, the effect of temperature must be 
included in these expressions for the displacement. 

The constant of integration which enters the expression for 
ff> f — <£, also enters in the last two equations for the displace- 
ment. The value of this constant must be known in order to 
determine the displacement. Besides the constant, there is 
also an unknown moment in M which must be determined. 

The applied forces acting on the beam are fully given, and 
are taken, as before stated, in the plane of mean fibre. The 
reactions at the points of support are not known, and must be 
determined. 

Let Xi represent the algebraic sum of all the components 
of the applied forces parallel to the axis of X ; Y t the sum of 
the components parallel to the axis of ,Y ; 1^ and R 2 the 
vertical components of the reactions at A and B, respectively ; 
and Q x and Q 2 the horizontal components of these reactions. 

For equilibrium, there obtains, 

X t + Qi - Q 2 = 0, ) 
T 1 -E 1 -E 2 = J L . . (115) 

/jl x — RA + Q 2 4 = 0. ) 

In the last equation, /^ represents the sum of the moments 
of the known applied forces taken with respect to the point 
of support, A, l x , and Z 2 , the lever arms of E^ and Q 2 , with 
respect to the same point. 

We have three equations and four unknown quantities. By 
introducing the condition that the point B, shall occupy the 



158 



CIVIL ENGINEERING. 



same position after the application of the forces as it had be- 
fore, that is, he fixed, a fourth equation may be obtained, and 
the problem made determinate. 

To express this last condition, let x 1 and y x be the co-ordi- 
nates of the extremity B (Fig. 40), x and y the co-ordinates 







a 


\ 


h 










^^^^^ 


^C 








JZ 










I \ 








\ 


.•'» 


V, 










,' 


\ 










/ 


\ 








s* 




\ 


\ 




Y 


/ 








\ 











Fig. 40. 

of any point as D, and <£ the angle made by the tangent line at 
D with the axis of X. Represent by T x the sum of the com- 
ponents of the applied forces parallel to the tangent DT, and 
by \x the sum of the moments of the applied forces with re- 
spect to to the section at D. 

The bending moment at D will be 

M = / 4 + Q 2 (y 1 -y)-E a (« l -aj) . . (116) 

and for the force acting in the direction of the tangent DT, 



P — T x + Q 2 cos <£ 4- R^ sin <£. 



(117) 



In these two equations, whenever the applied forces are given, 
/x, T,, y x — y y and x x — a?, are known functions; but itj and 
Q 2 are unknown constants. 

But from the third of equations (115) we have 

_, Pi + Q 2 ^2 

K* = 1 } 

which substituted in the expressions just obtained for M and 
P give them in terms of one unknown constant and known 
functions. 

We are now able to find the values of the constant of in- 



CURVED BEAMS. 159 

tegration before referred to, and the component Q 2 . Know- 
ing the latter, those of Q 1? 1^, and 1^ are easily found. 

226. Having found all the external forces acting on the 
beam, the strain on any cross-section may be determined, and 
its area calculated. 

The strain on the unit of area of the cross-section, at the 
distance y from the neutral axis, is 

R A + T and S = A' 

iii which P and F are the components of the external forces, 
perpendicular and parallel to the plane of cross-section; A, 
the area of the cross-section ; I, its moment of inertia ; and 
H the bending moment of the external forces with respect to 
the neutral axis of the cross-section. 

227. In chapters IV. and V. of his "Cours de Mecanique 
Appliquee," M. Bresse has given a complete discussion of the 
strains in curved beams resting on two points of support, pro- 
duced by external forces acting in the plane of mean fibre ; 
the cross-section of the beam being uniform and the curve of 
mean fibre a circular arc. 

Pie has deduced exact formulas for the horizontal thrust, 
Q 2 , and reduced these formulas to forms of easy application 
for the cases most commonly used. He has besides con- 
structed tables containing the values of the quantities found 
in the formulas^ under the different., suppositions, usually 
made. w-^> 4 £&* 6 ■« - **»- *-**— K^k M*-w~u- (^vy^r^UA^l^*^ x f 

If the^beam is loaded symmetrically with reference to^its clL^( ^KC / 
middle point, or strained by vertical loads only, Q x and Q 2 are 
equal. 

The following formula for a load uniformly distributed 
over the beam, along the mean fibre, when the rise, H C, is 
small compared with the span, A B, is given by him : 






I 150 r 

\i +i s 7 / 



<&=<& = wp+^g -— 



in which w is the load on the unit of length of the curve ; p, 
the radius of the curve of mean fibre ; <£, the half of the 
angle, A B, included between the radii drawn to the ex- 
tremities A and B ; 21, the length of the chord, A B ; /, the 
rise, H C ; and k, the radius of gyration of the cross-section of 
the beam. 



160 



CIVIL ENGINEEKING. 



And under the same circumstances, the load being dis- 
tributed on the beam uniformly over the chord A B or a 
horizontal tangent at C, he gives the following formula : 



W>1 — W>2 



wl 2 



7 7* 



V , 15 ^ / 



(119) 



228. Approximate method of determining the strains on 
a curved beam, uniformly loaded along a horizontal straight 
line ; the beam resting on two points of support in the same 
horizontal plane. 

Assume that the curve of mean fibre is a parabolic arc, 
and that the bending moment at the middle point is equal to 
zero. 

Let A V be the curve of half of the mean fibre of the beam 
(Fig. 41). 

Take the origin of co-ordinates at the middle point V, the 
tangent at V for the axis of X, and the perpendicular VY for 




Fig. 41. 

the axis of Y. Let D and D' be any two consecutive points 
whose abscissas are x and x . Denote by I the half-span A Y, 
by f the rise V Y, and by w the weight on the unit of length 
measured on V X. 

Suppose the beam cut in two at V, and a horizontal force 
II acting at V to preserve its shape. 

The resistance offered at any section, as D, to the compres- 
sion produced by the load wu\ is in the direction of the tan- 
gent to the curve of mean fibre at this point. The external 
forces therefore acting on the segment D V are the horizontal 
force II, the weight wx, and the resistance at D which we 
denote by P. 






ci 






, 






\ Y \ 






r- 



<;-. 
-^^ 



4S^ * 



G> ,s> 



6 -J 



3 
? 









> "t 



- 



i ■ ■; * 







3 1 r 






:> 



L 



} i 



9 i £ 1 



I 6 
s £ 

! ^ 
i 

+ ■ 



i 



.^ 

-??. 

3 

^ 



j 

V-, l 



<--> ! 



«) .:' 



IS 1 









i 















\ ■ 



! A 











K 


*. ; 


'3 


'. 







~> 









3 



*o!^ 



'- 



! • : -~ 






3 



J 


















L 






i 















i 



5 

- 



j 

7$ 






i 



i ? -- 



-J 



o 






I , t t 



CURVED BEAMS. 161 

Since the curve, AV, is part of a parabola whose vertex is 
at V, the tangent drawn at D cuts the axis of X at T, midway 
between V and x, This is the point through which the weight 
wx acts. Since there is an equilibrium in the system of 
forces acting on the arc D V, the intensities of these forces II. 
P, and wx must be proportional to the sides of the triangle 
D#T. Since D H and D'H are respectively parallel to Tx and 
Da?, we have 

Tx: Dxy. HD : D'H, 

or H : wx '. '. dx : dy, 

whence dy = 75 ®dx* 



H 



Integrating, we obtain 



w 
y = m a? + C (120) 

Taking this between the limits x = and x = l 9 there re- 
sults 

whence . H = ^ (121) 

which is the coefficient outside of the parenthesis in the ex- 
pression for Q 2 in eq. (119). 

This value for II may be deduced directly by moments, 
For we have 

H x AX = wVX x iVX, 
or Bf- — , 

whence H = - Q „• 

But p = vw + .«w; 

and substituting in which the value just found for H, we get 



P = ^Vra + a?. . . . (122) 



11 



tio 



162 CIVIL ENGINEERING. 

These expressions show that P is least at V and greatest at 
A, and that IT is the same throughout. The value for H is 
independent of the form of the curve of mean fibre, whether 
parabolic, circular, or other shape. 



CURVED BEAMS WITH THE ENDS FIRMLY FIXED. 

229. The curved beam in the foregoing discussion has had 
the analogous position of a straight beam resting on two sup- 
ports. In each of these cases the beam has been regarded as 
continuous between the points of support and the horizontal 
distance between these points as constant. 

If, in addition, the condition be imposed that the cross- 
sections at the points of support he fixed so that they shall 
not move under the action of the external forces, the case 
becomes analogous to that of a straight beam whose ends are 
firmly imbedded in a wall. And there will be, as in that case, 
an unknown moment at the points of support, whose value 
must be found before the strains on the beams can be deter- 
mined. Having found this, the processes of obtaining the 
strains and calculating the dimensions of the beam are ana- 
logous to those already used. 



PART III. 



CHAPTEK VIII. 



FRAMING. 



230. The art of construction consists mainly in giving to 
a structure the proper degree of strength with the least 
amount of material necessary for the purpose. If any piece 
be made stronger than is necessary, the superfluous weight of 
this piece will in general be transmitted to some other part, 
which will be required in consequence to sustain a greater 
load than it should. Hence, the proper distribution and 
sizes of the different parts of a structure should be de- 
termined. 

A frame is an arrangement of beams, bars, rods, etc., 
made for sustaining strains. The art of arranging and fit- 
ting the different pieces is called framing, and forms one of 
the subdivisions of the art of construction. It follows, then, 
from the previous remark, that the object to be attained in 
framing is to arrange the pieces, with due regard to lightness 
and economy of material, so that they shall best resist, with- 
out change of form in the frame, the strains to which the 
latter may be subjected. 

231. The principal frames employed by engineers are those 
used in bridges, centres for arches, coffer-dams, caissons, 
floors, partitions, roofs, and staircases. 

The materials used in their construction are generally tim- 
ber and iron. The latter, in addition to superior strength, 
possesses an advantage over wood in being susceptible of re- 
ceiving the most suitable form to resist the strains to which it 
may be subjected. 

When the principal pieces of a frame are of timber, the 
construction belongs to that branch of framing known as 
carpentry. 

The combination of the pieces, and the shape of a frame 



164 CIVIL ENGINEERING. 

will depend upon the purposes for which the frame is to be 
adapted and upon the directions of the straining forces. 

One of the main objects in the arrangement of a frame is 
to give the latter such a shape that it will not admit of change 
in its figure when strained by the forces which it is intended 
to resist. This is usually effected by combining its parts so 
as to form a series of triangular figures, each side of the 
latter being a single beam. If the frame has a quadrilateral 
shape, secondary pieces are introduced either having the 
positions of the diagonals of the quadrilateral, or forming 
angles with the upper and lower sides of the frame. These 
secondary pieces are called braces. When they sustain a 
strain of compression they are termed struts ; of extension, 
ties. 

The strength, and hence the dimensions, of the pieces will 
be regulated by the strains upon the frame. Knowing the 
strains and the form of the frame, the amount of strain on 
each piece can be deduced, and from this the proper form 
and particular dimensions of each piece. 

The arrangement of the frame should be such that, after 
being put together, any one piece can be displaced without 
disconnecting the others. 

"When practicable, the axes of the pieces should be kept in 
the plane of the forces which act to strain the frame, and the 
secondary pieces of the frame should be arranged to transmit 
the strains in the direction of their lengths. The pieces are 
then in the best position to resist the strains they have to 
transmit, and all unnecessary cross-strains are avoided. 

The essential qualities of a frame are, therefore, strength, 

iffness, lightness, and economy of material. 



JOINTS. 

232. The joints are the surfaces at which the pieces of a 
frame touch each other ; they are of various kinds, according 
to the relative positions of the pieces and to the forces which 
the pieces exert on each other. 

Joints should be made so as to give the largest bearing sur- 
faces consistent with the best form for resisting the particular 
strains which they have to support, and particular attention 
should be paid to the effects of contraction and expansion in 
the material of which they are made. 

In planning them the purpose they are to serve must be 
kept in mind, for the joint most suitable in one case would 
oftentimes be the least suitable in another. 



FISH JOINTS. 165 



JOINTS IN TIMBER WORK. 

233. In frames made of timber, the pieces may be joined 
together in three ways ; by connecting them, 

1. End to end ; 

2. The end of one piece resting upon or notched into the 
face of another ; and 

3. The faces resting on or notched into each other. 

I. Joints of beams united end to end, the axes of the 
beams being in the same straight line. 

234. First. Suppose the pieces are required to resist strains 
in the direction of their length. 

This case occurs when in large or long frames a single 
piece of the required length cannot be easily procured. 

The usual method of lengthening is in this case by fishing 
or scarfing, or by a combination of the two. 



FISH-JOINTS. 

When the beams abut end to end and are connected by 
pieces of wood or iron placed on each side, and firmly bolted 
to the timbers, the joint is called a fish-joint, and the beam 
is said to be fished. 

This joint is shown in Fig. 42, and makes a strong and 
simple connection. 

^ • frri n rn r-frf , ESQ rrr-i rm 



I 



! 6 ii 



Fig. 42 — Represents the manner in which two beams a and b are fished by- 
side pieces c and d bolted to them. 

When the beams are used to resist a strain of compression, 
the fish-pieces should be placed on all four sides, so as to pre- 
vent any lateral movement whatever of the beams. 

If the strain be one of tension, it is evident that the strength 
of the joint depends principally upon the strength of the 
bolts, assisted by the friction of the fish-pieces against the 
sides of the timber. 



166 



CIVIL ENGINEERING. 



The dependence upon the bolts may be much lessened by 
notching the fish-pieces npon the beams, as shown on the 



I 



@= 



=© 



<§> 



3> 



@= 



3> 



Fig. 43 — Represents a joint to resist extension, iron rods or bars being used 
to connect the beams instead of wooden fish-pieces. 

upper side of the piece in Fig. 44. Or by making use of 
keys or blocks of hard wood inserted in shallow notches made 
in both the beam and fish-piece, as shown on the lower side 
of the piece in the same figure. 



\ 



^^ 



A 



7 



Fig. 44 — Represents a fished joint in which the side pieces c and d are either 
let into the beams or secured by keys e, e. 

Care should be taken not to place the bolts too near the 
ends of the pieces. The sum of the areas of cross-sections of 
the bolts should not be less than one-fifth that of the beam. 



SCAKF-JOINTS. 

In these joints the pieces overlap each other and are bolted 
together. The form of lap depends upon the kind of strain 
to which the beam is to be subjected. 

Fig. 45 is an example of a simple scarf -joint that is some- 
times used when the beam is to be subjected only to a slight 




Fig. 45. 



strain of extension. A key or folding wedge is frequently 
added, notched equally in both beams at the middle ; it serves 
to bring the surfaces of the joint tightly together. 



FISH AND SCARF JOINTS. 



167 



This joint is often made by cutting the beams in such a 
manner as to form projections which fit into corresponding 
indentations. A good example, in which two of these notches 

46. 



are made, is shown in Fig. 




Fig. 46. 

The total lap shown in this figure is ten times the thickness 
of the timber, and the depth of the notches at A and B are 
each equal to one-fourth that of the beam. The bolts are 
placed at right angles to the principal lines of the joint. 

This is a good joint where a strain of tension of great 
intensity is to be resisted, as by the notches at A and B, one- 
half of the cross-section of the beam resists the tensile strain. 



COMBINATION OF FISH AND SCARF JOINTS. 

The joint shown in Fig. 47 is a combination of the fish and 
scarf -joints, and is much used to resist a tensile strain. 



> 


_[JJ 


rfh C rfl-, 
i 0? jj 


d y 


F#=D— 


( 


;; HI ;; 
a 7. u= 


U— 1 



Fig. 47 — Represents a scarf -joint secured by iron fish-plates c, c, keys 
d, d t and bolts. 

235. Second. Suppose the pieces are required to resist a 
transverse strain. 

In this case the scarf-joint is the one generally used, and it 
is then formed sometimes by simply halving the beams near 
their ends,-as shown in Fig. 47. 

The more usual and the better form of joint for this case is 
shown in Fio;. 48. 



Fig. 48— Represents a scarf -joint for a cross-strain, fished at bottom by 
a piece of timber c. 



168 CIVIL ENGINEERING. 

In the upper portion of this joint the abutting surfaces are 
perpendicular to the length of the beam and extend to a depth 
of at least one-third and not exceeding one-half that of the 
beam. In the bottom portion they extend one-third of the 
depth and are perrjendicular to the oblique portion joining 
the upper and lower ones.- 

The lower side of the beam is fished by a piece of wood or 
iron plate, secured by bolts or iron hoops, so as to better resist 
the tensile strain to which this portion of the beam is sub- 
jected. 

Third. Suppose the piece required to resist cross-strains 
combined with a tensile strain. 

The joint, frequently used in this case, is shown in Fig. 49. 



Fig. 49 — Represents a scarf -joint arranged to resist a cross-strain and one 
of extension. The bottom of the joint is fished by an iron plate ; and a 
folding wedge inserted at c serves to bring all the surfaces of the joint 
to their bearings. 

236. Iii the previous cases the axes were regarded as being 
in the same straight line. If it be required to unite the ends 
and have the axes make an angle with each other, this may be 
done by halving the beams at the ends, or by cutting a mortise 
in the centre of one, shaping the end of the other to lit, and 
fastening the ends together by pins, bolts, straps, or other 
devices. The joints used in the latter case are termed 
mortise and tenon joints. Their form will depend upon 
the angle between the axes of the beams. 

II. Joints of beams, the axes of the beams making an 
angle with each other. 



MOETISE AND TENON JOINTS. 

237. When the axes are perpendicular to each other, the 
mortise is cut in the face of one of the beams, and the end 
of the other beam is shaped into a tenon to fit the mortise, as 
shown in Fig. 50. 

When the axes are oblique to each other, one of the most 
common joints consists of a triangular notch cut in the face 
of one of the beams, with a shallow mortise cut in the bottom 



MORTISE AND TENON JOINTS. 



169 



of the notch, the end of the other beam being cut to fit the 
notch and mortise, as shown in Fig. 51. 



K 



B 



Fig. 50 — Represents a mortise and tenon joint when the axes 
of the beams are perpendicular to each other. 
«, tenon on the beam A. 

b, mortise in the beam B. 

c, pin to hold the parts together. 

In a joint like this the distance ab should not be less than 
one-half the depth of the beam A ; the sides ab and be should 
be perpendicular to each other when practicable ; and the 




Fig. 51 — Represents a mortise and tenon joint when the 
axes of the beams are oblique to each other. 



thickness of the tenon d should be about one-fifth of that of 
the beam A. The joint should be left a little open at c to 
allow for settling of the frame. The distance from b to the 
end D of the beam should be sufficiently great to resist safely 
the longitudinal shearing strain caused by the thrust of the 
beam A against the mortise. 
Denote by 

H the component of the thrust, parallel to the axis of 

the beam B D ; 
b the breadth in inches of the beam B D ; 



170 CIVIL ENGINEERING. 

I the distance in inches from the mortise b to the end 
D ; and 

S the resistance per square inch in the beam B to lon- 
gitudinal shearing. 
The total resistance to shearing will be S x hi, hence 

S x bl = H, from which we have 

H 



1 = 



SxJ' 



The value of S for the given material, Art. 166, being sub- 
stituted in this expression, will give the value for £, when the 
strain just overcomes the resistance of the fibres. In this 
case the factor of safety is ordinarily assumed to be at least 
four. Therefore the value of I, when the adhesion of the 
fibres is depended upon to resist this strain, will be : 

4H 

I =z 7 -, S being taken from the tables. 

A bolt, ef, or strap, is generally used to make the joint 
more secure. 

In both of these cases the beam A is subjected to a strain 
of compression, and is supported by B. If we suppose the 
beams reversed, A to support B, the general principles for 
forming the joints would remain the same. 

Suppose the axes of the beams to be horizontal, and the 
beam A to be subjected to a cross-strain, the circumstances 
being such that the end of the beam A is to be connected with 
the face of the other beam B. 

In this case a mortise and tenon joint is used, but modified 
in form from those just shown. 

To weaken the main or supporting beam as little as possi- 
ble, the mortise should be cut near the middle of its depth ; 
that is, the centre of the mortise should be at or near the neu- 
tral axis. In order that it should have the greatest strength, 
the tenon should be at or near the under side of the joint. 

Since both of these conditions cannot be combined in 
the same joint, a modification of both is used, as shown in 
Fig. 52. 

The tenon has a depth of one-sixth that of the cross-beam 
A, and a length of twice this, or of one-third the depth of the 
beam. The lower side of the cross-beam is made into a shoul- 
der, which is let into the main beam, one half the length of 
the tenon. 

Double tenons have been considerably used in carpentry. 






FASTENINGS. 3 71 

As a rule they should never be used, as both are seldom in 
bearing at the same time. 



A 



Fig. 52. — A, the cross-beam. 

B, cross-section of main beam. 
t, the tenon. 

III. Joints used to connect beams, the faces resting on 
or notched into each other. 

238. The simplest and strongest joint in this case is made 
by cutting a notch in one or both and fastening the beams to- 
gether. 

If the beams do not cross, but have the end of one to rest 
upon the other, a dove-tail joint is sometimes used. In this 
joint, a notch trapezoidal in form, is cut in the supporting 
beam, and the end of the other beam is fitted into this notch. 

On account of the shrinkage of timber, the dove-tail joint 
should never be used except in cases where the shrinkage in 
the different parts counteract each other. 

It is a joint much used in joiner's work. 

239. The joints used in timber-work are generally composed 
of plane surfaces. Curved ones have been recommended 
for struts, but the experiments of Hodgkinson would hardly 
justify their use. The simplest forms are as a rule the best, 
as they afford the easiest means of fitting the parts together. 



FASTENINGS. 

240. The pieces of a frame are held together at the joints 
by fastenings, which may be classed as follows : 

1. Ping, including nails, spikes, screws, bolts, and wedges ; 

2. Straps and tiebars, including stirrups, suspending-rods, 
etc. ; and 

3. Sockets. 

These are so well known that a description of them is un- 
necessary. 



172 CIVIL ENGINEERING. 



GENERAL RULES TO BE OBSERVED IN THE CONSTRUCTION OF JOINTS. 

241. In planning and executing joints and fastenings the 
following general principles should be kept in view : 

I. To arrange the joints and fastenings so as to weaken as 
little as possible the pieces which are to be connected. 

II. In a joint subjected to compression, to place the 
abutting surfaces as nearly as possible perpendicular to the 
direction of the strain. 

III. To give to such joints as great a surface as practicable. 

IV. To proportion the fastenings so that they will be equal 
in strength to the pieces they connect. 

Y. To place the fastenings so that there shall be no danger 
of the joint giving way by the fastenings shearing or crushing 
the timber. 

JOTNTS FOR IRON-WORK. 

242. The pieces of an iron frame are ordinarily joined by 
means of rivets, pins, or nuts and screws. 



RIVETED JOINTS. 

243. A rivet is a short bolt or pin, of iron or other malle- 
able material, with a head, so that it can be inserted into 
holes made in the pieces to be fastened together, and the point 
of the bolt can be spread out or beaten down closely upon the 
piece by pressure or hammering. This operation is termed 
riveting 1 , and is performed by hand or by machinery. By 
hand, it is done by a succession of blows from a hammer. By 
the riveting machine as ordinarily used, it is effected by press- 
ing the heated bolt into the hole by a single stroke. If a ma- 
chine uses a succession of blows, the operation is then known 
as snap-riveting. By many it is claimed that machine 
riveting possesses great superiority over that by hand, for 
the reason that the rivets more completely fill the holes, and 
in tills way become an integral part of the structure. It is 
doubtful if it possesses the advantage of superior strength to 
any marked degree. It does certainly possess, however, the 
advantage of being more cpiickly executed without damage 
to the heads of the rivets. 

The holes are generally made by punching, are about one- 
twentieth of an inch larger than the diameter of the rivet, and 



NUMBER OF RIVETS. 173 

are slightly conical. The diameter of the rivet is generally 
greater than the thickness of the plate through which the hole 
is to be punched, because of the difficulty of punching holes 
of a smaller size. Punching injures the piece when the latter 
is of a hard variety of iron, and for this reason engineers of ten 
require that the holes be drilled. Drilling seems to be the bet- 
ter method, especially when several thicknesses of plates are 
to be connected, as it insures the precise matching of the rivet 
holes. The appearance of the iron around a hole made by 
punching gives a very fair test of its quality. 

When two or more plates are to be riveted, they are placed 
together in the proper position, with the rivet-holes exactly 
over one another, and screwed together by temporary screw- 
bolts inserted through some of the holes. The rivets, heated 
red-hot, are then inserted into the holes up to the head, and 
by pressure or hammering, the small end is beaten down fast 
to the plate. In a good joint, especially when newly riveted, 
the friction of the pieces is very great, being sufficient to sus- 
tain the working-load without calling into play the shearing 
resistance of the rivets. In calculating the strength of the 
frame, this amount of strength due to friction is not consid- 
ered, as it cannot be relied on after a short time in those cases 
where the frame is subjected to shocks, vibrations, or great 
changes of temperature. 



NUMBER AND ARRANGEMENT OF RIVETS. 

244. The general rule given for the number is that the 
sum of the areas of the Gross-sections of the rivets shall he 
equal to the effective sectional area of the plate after the holes 
hai)e been punched. This rule is based on the theory that the 
resistance to shearing strain in the rivet is equal to the tena- 
city of the plate. 

To determine the proper distance between the rivets 
in the direction of any row, so that the strength of the rivets 
in any single row shall be equal to the strength of the section of 
the plate along this row after the holes have been punched, 
let 

d, be the diameter of the rivet ; 

c, the distance from centre to centre of the rivets ; 

a, the area of cross-section of the rivet ; 

A', the effective area of cross-section of the plate along the 
row of rivets ; and 

t, the thickness of the iron plate. 



174 CIVIL ENGINEEKING. 

It has been assumed that 

T = S, 
and the rule requires that 

TA' = Sx«, or -K- = -j-, = 1. 

We have 

a _ \ird % _ 

A 7 ~~ t{c-d) ~ 7 
whence 

e = i —+d, (123) 

for the distance from centre to centre of the consecutive 
rivets in any one row. 

English engineers, in practice, use rivets whose diameters 
are -§-, f, -J, 1, 1J-, and 1^ inches, for iron plates J, T 5 -g-, ■§-, £, -§-, 
and f inches thick, respectively, and take the distance from 
centre to centre at 2 diameters for a strain of compression, 
and 2J diameters for extension. The distance of the centre 
of the extreme rivet from the edge of the plate is taken be- 
tween 11 and 2 diameters. 

Instead of assuming the resistance to shearing in the rivet 
equal to the tenacity of the iron plate, a better rule would be 
to make the product arising from multiplying the sum of the 
■areas of the cross-sections of the rivets, by the amount of 
shearing strain allowed on each unit, equal to the maximum 
strain transmitted through the joint. 

If the strain was one of compression in the plates and the 
ends exactly fitted, the only riveting required would be that 
necessary to keep the plates in position. As the workman- 
ship rarely, if* ever, admits of so exact fitting, the rivets 
should be proportioned by the rules just given. 

245. The size of the head of a rivet depends upon the 
diameter of the rivet. It is usually circular in form, and 
should have a diameter not less than twice, and a thickness at 
the centre not less than one-half, of the diameter of the rivet. 



oo 
oo 
o o 



oo 
oo 
oo 



Fro. 53. 

246. Various methods are used in the arrangement of the 
rivets. The arrangement often used for lengthening a plate 
is shown in Fig. 53. This method is known as " chain rivet- 
ing." 



ARRANGEMENT OF RIVETS. 



175 



Fig. 54 shows another method used for the same purpose, 
in which the number of rivets is the same as in the previous 
example, but there is a better disposition of them. 





Fig. 54. 



Figs. 55 and 56 show the arrangement of the rivets often 
used to fasten ties to a plate. 



O O 

9, ° 
OO 

O 



l/~V 



ooo 
ooo 
o o 



W*%J 



Fig. 55. 




Fig. 50. 



Figs. 57, 58, and 59 show in plan the forms of several 
kinds of riveted joints. 



Fig. 57. 



Fig. 57 shows the single shear-joint or single lap-joint. 



-£^ ^N- 



Fig. 58. 



Fig. 5S bhows the ordinary fish-joint. In this joint the 
fish or cover plates are placed on each side, and have a thick- 



176 CIVIL ENGINEERING. 

ness of half that of the plates to be connected ; sometimes 
only one cover plate is used, and then the connection is 
known as the butt-joint. 





i 


^ 


^7^ 




*~\ 


/*-v 


/^V ^N 


I 


■v :: ;: i :: :i :: : 


! ! I 


V- 


% :: ,; ;: ii I m i 


! ! i 


s, 


% i; ii II il ii i 


I II : 


V 




I 


n 


; i 


, i 


1 1 


! ! 






i 






\s 




\~s 


v— ' 


^y 


" \~s \^ 


\s 



Fig. 59. 



When several plates are to be fastened together, the method 
shown in Fig. 59 is the one ordinarily used. 



EYE-BAR AND PIN JOINTS. 

247. A simple and economical method of joining flat bars 
end to end when subjected to a strain of extension, is to con- 
nect them by pins passing through holes or eyes made in the 
ends of the bars. 

When several are connected end to end, they form a flexi- 
ble arrangement, and the bars are often termed links. 

This method of connecting is called the eye-bar and pin, 
or link and pin joint, and is shown in plan in Fig. 60. 



Z 



Fig. 60. 

The bar at the end should be so formed that it would be 
uo more liable to break there than at any other point of the 
bar. The following are the dimensions in the case where the 
head has the same thickness as the bar. 

If the width of the bar be taken as equal to 1 . 

The diameter of the eye should equal . . 7."). 

Depth of head beyond the eye should equal 1 . 

Sum of the sides of the head through eye should equal 1.25. 

Kadi us of curve of neck should equal 1.5. 

Hence, for a bar eight inches wide, the dimensions would 
be as shown in Fig. 61. 



SCEEW-BOLTS. 



177 



By this rule the pin has a diameter which gives a sufficient 
bearing surface, the important point to be considered. 




Fig. 61 



There should be a good fit between the pin and eye, espe- 
cially in structures subjected to shocks, hence the conditions 
of manufacture and the quality of material and workmanship 
should be of the strictest kind, and closely observed. 



SCREW-BOLT JOINTS. 

248. The connection by nut and screw is simple and 
economical. 

The strength of a bolt or rod on which a screw is made, 
when subjected to a shearing strain, is determined as in the 
case of rivets or pins. In case of a tensile strain the strength 
is measured by the area of cross-section of the spindle inside 
the thread. 

The resistance offered to stripping by the nut depends upon 
the form of the thread and the depth of the nut. In order 
that this resistance should be equal to that offered by the bolt 
to being pulled apart, the length of the nut should be at least 
equal to one-half the diameter of the screw. 

The following proportions have been recommended by the 
Franklin Institute : 







Six-sided nu 


. — Length of 






Diameter of 


No. of threads 






Depth of 


Depth of 


bolt in inches. 


per inch. 


Long diameter, 


Short diameter, 


head. 


nut. 


i 


13 


1 


1 


i 6 


i 


f 


10 


I'h 


H 


f 


I 


1 


8 


H 


H 


tt 


1 


H 


6 


21 


2| 


ifV 


H 


2 


4i 


31 


3i 


IrV 


2 


2i 


4 


4* 


H 


Ht 


2i 


3 


3£ 


51 


4f 


2A 


3 



12 



178 CIVIL ENGINEEEING. 



SIMPLE BEAMS. 



249. One of the most common and simple use of frames 
is that in which the frame is supported at its extremities and 
subjected only to a transverse strain. 

When the distance between the points of support, or the 
bearing, is not very great, frames are not necessary, but beams 
of ordinary dimensions are strong and stiff enough to resist 
the cross- strains arising from the load they support, without 
bending beyond the allowed limits. The load placed upon 
them may be uniformly distributed, or may act at a point ; 
in either case the strains produced, and the dimensions of the 
beam to resist them, can be easily determined. (Arts. 177 
and 179.) The usual method followed is to place the beams 
in parallel rows, the distance apart depending on the load 
they have to support. The joists of a Hoor, the rafters of a 
roof, are examples of such cases. 

The depth of a beam used for this purpose is always made 
much greater than its breadth, and arrangements are always 
made to prevent its twisting or bending laterally. In the 
joists of a floor it is usual to place short struts or battens in a 
diagonal direction between them, joining the top of one joist 
with the bottom of the next. The extremities of the beams 
should be firmly fixed on the points of support. 



SOLID BUILT BEAMS. 

250. A solid beam is oftentimes required of greater 
breadth or thickness than that of any single piece of timber. 
To provide such a beam it is necessary to use a combination 
of pieces, consisting of several layers of timber laid in juxta- 
position and firmly fastened together by bolts, straps, or other 
means, so that the whole shall act as a single piece. This is 
termed a solid built beam- 



Fig. G2. 



When two pieces of timber are built into one beam having 
twice the depth of either, keys of hard wood arc used to resist 
the shearing strain along the joint, as shown in Fig. 62, 



SOLID BUILT BEAMS. 



179 



Tredgold gives the rale that the breadth of the key should 
be twice its depth, and the sum of the depths should be equal 
to once and a third the total depth of the beam. 

It has been recommended to have the bolts and the keys on 
the right of the centre make an angle of 45° with the axis of 
the beam, and those on the left to make the supplement of 
this angle. 

The keys are sometimes made of two wedge-shaped pieces 
(Fig. 63), for the purpose of making them fit the notches 




Fig. 63— Represents the folding wedges, a, b, let into a notch in 
the beam c. 



more snugly, and, in case of shrinkage in the timber, to allow 
of easy readjustment. 

When the depth of the. beam is required to be less than the 
sum of the depths of the two pieces, they are often built into 
one by indenting them, the projections of the one fitting 
accurately into the notches made in the other, and the two 
firmly fastened together by bolts or straps. The built beam 
shown in Fig. 64 illustrates this method. In this particular 
example the beam tapers slightly from the middle to the 
ends, so that the iron bands may be slipped on over the ends 
and driven tight with mallets. 




Fig. 64— Represents a solid built beam, the top part being of two pieces, 5, b, 
which abut against a broad flat iron bolt, a, termed a king-boLt. 



When a beam is built of several pieces in lengths as well 
as in depth, they should break joints with each other. The 
layers below the neutral axis should be lengthened by the 
scarf or fish joints used for resisting tension, and the upper 



180 



CIVIL ENGINEERING. 



ones should have the ends abut against each other, using plain 
butt joints. 

Many builders prefer using a built beam of selected tim- 
ber to a single solid one, on account of the great difficulty of 
getting the latter, when very large, free from defects ; more- 
over, the strength of the former is to be relied upon, although 
it cannot be stronger than the corresponding solid one if per- 
fectly sound. 



FRAMING WITH INTERMEDIATE POINTS OF SUPPORT. 



251. If the bearing be great, the beam will bend under 
the load it has to support, and to prevent this it is necessary 
to provide intermediate points of support. These points of 
support may be below the beam, or they may be above it. 

The simplest method, when practicable, is to place at 
suitable intervals under the beam upright pieces to act as 
props or shores. 

When these cannot be had, but points of support can be 
obtained below those on which the beam rests, inclined struts 
may be used. 

These may meet at the middle point of the beam, divid- 
ing it into two equal parts. The beam is then said to be 
braced, and is no longer supported at two points, but rests 
on three. 

The struts may be placed so as to divide the beam (Fig. 65) 
into three parts, being connected with it by suitable joints. 







Fig. 65. 



The bearing of the beam may be reduced by placing under 
it and on the points of support (Fig. 6C>) short pieces, termed 
corbels. These, when long, should be strengthened by struts, 
as shown in the figure. 

In some cases the beam is strengthened by placing under 



OPEN-BUILT BEAMS. 



181 



the middle portion a short piece, termed a straining beam 

(Fig. 67), which is supported by struts. 





Fig. 66 — A horizontal beam, c, resting on vertical posts, a a, with 
corbels, d d, and struts, e e. 

These methods may be combined when circumstances re- 
quire it, and the strains on the different parts can be deter- 
mined. It is well to remember that placing equal beams over 





f 



Fig. 67 — A horizontal beam, c, strengthened by a straining beam, /. 

each other only doubles the strength, unless they are firmly 
connected so as to act as one beam, in which case the combi- 
nation follows the law already deduced, that is, the strength 
will he four times as great. 



OPEN -BUILT BEAMS. 

252. An open-built beam, or truss, is a frame in which 
two beams, either single or solid built, with openings between 
them, are connected by cross and diagonal pieces, so that the 
whole arrangement acts like a single beam in receiving and 
transmitting strains. 

These f rames are largely used in bridge building, and their 
details will be considered under that head. 

The king-post truss is one of the simplest forms of frames 
belonging to this class. 

This truss is employed when there are no points of support 
beneath the beam which can be used, and when the middle 
of the beam is sustained by suspension from a point above. 

The arrangement consists of two inclined pieces framed 



182 



CIVIL ENGINEERING. 



into the extremities of the beam, and meeting at an angle 
above, from which the middle of the beam is supported by a 
third piece. This combination is shown in Fig. 68. 




Fig. 68. 

The construction is simple and the frame is rigid. It is 
frequently employed in roofs and in bridges of short span. 

In the earlier constructions the third piece, g, was made of 
wood, and resembled a post, hence the name of king-post. 
The strain it sustains is one of tension, and in modern con- 
structions an iron-rod is generally used. It would be better 
if a more appropriate name were given, since the term post 
conveys to the mind an impression that the strain is one of 
compression. 

When the suspension piece is made of timber, it may be a 
single piece framed into the struts, and the foot connected 
with the beam by a bolt, an iron stirrup, or by a mortise and 
tenon joint ; or it may be composed of two pieces bolted 
together, embracing the heads of the struts and the supported 
beam. In the latter case, these pieces are called bridle- 
pieces, two of which are shown in Fig. 69. 







Fig. 69. 



When two points of support are necessary, the arrangement 
known as the queen-post truss may bo used. It consists of 
two struts framed into the extremities of the beam, and abut- 
ting against a short straining beam (Fig. 69). The suspen- 



STRAINS ON FRAMES. 183 

sion pieces being either of iron or wood, single or doable, as 
in the king-post truss. 

The same remarks about the name apply to this combina- 
tion. 

Both of these trusses may be inverted, thus placing the 
points of support beneath the beam. This change of position 
changes the character of strains on the different parts, but 
does not affect their amount, which is determined in the same 
way. 

Points of support above and beneath may be obtained by o 
the use of curved beams. 



METHODS OF CALCULATING STRAINS ON FRAMES. 



253. It has been previously stated that to prevent a change 
of form in a quadrilateral frame, secondary pieces are intro- 
duced for the purpose of dividing the frame into two or more 
triangular figures. 

In all frames where rigidity is essential to stability, this in- 
troduction of braces is necessary, as the triangle is the only 
geometrical figure which, subjected to a straining force, 
possesses the property of preserving its form unaltered as 
long as the lengths of its sides remain constant. 

The simplest form of frame is the triangular, and will be 
first used in this discussion. 

254. As a preliminary step, let the strains in an inclined 
beam, arising from a force acting in the plane of its axis, be 
determined. 

For example, take 

An inclined beam with the lower end resting against an 
abutment and the upper end against a vertical wall, and sup- 
porting a weight, IP, applied at any point. 

Fig. 70 represents the case. 

Denote by 

I, the length of the axis, A B, of the beam ; 

n x I, the distance from A to the point C, where W is ap- 
plied; 

a, the angle between A B, and vertical line through C. 

Disregarding the weight of the beam, the external forces 
acting on it are the weight, AY, and the reactions at A and B. 

The reaction at B is horizontal ; let us represent it by H. 
Represent the horizontal and vertical components of the re- 
action at A, respectively by H' and W. 



184 



CIVIL ENGINEERING. 



These forces are all in the same plane, and the analytical 
conditions for equilibrium are 

H - H' = 0, and W - W = 0. 




Fig. 70. 



r> 



or 



Taking the bending moment about A, we have 
WxAD-HxBE = 0, 

, H X I cos a — W x 7il sin a, 

H = n W tan a , 



hence 



(124) 



The forces IT, H', W, and W act (afe-M in the plane of and 
obliquely to the axis, A B, and their effect is to produce de- 
flection and compression of the fibres of the beam. The 
strain arising from deflection will be dne to the algebraic sum 
of the perpendicular components, and that from compression 
will be due to the sum of the parallel ones. (Art. 217.) 

Resolve W and IT into components acting perpendicularly 
and parallel to the axis of the beam. Represent by P and 
P', and Q and Q', these components, see Fig. 71. 

kb = W = w. 
Ad = P, Ac = Q. 
Ap = 11/ = /iW tan a. 
Am = P' An = Q'. 



STRAINS ON FRAMES. 



185 



The perpendicular components kd and Am act in opposite 
directions, hence the strain arising from deflection will be due 



to their difference, P — P'. 




^n> 



Fig. 71. 



The parallel components kc and kn act in the same direc- 
tion, hence the strain of compression will be due to their sum, 

Q + Q'. 

Representing the force AY, by the line kb, we find the values 
of these components to be as follows : 

P = W sin a ; P' = n W tan a cos a — n W sin a ; 
Q = W cos a ; Q' = n W tan a sin a. 

Suppose the cross-section of the beam to be a rectangle of 
uniform dimension, the sides of which are respectively b 
and d, the plane of the latter being taken parallel to the 
direction of the force, W, we have 

Q + Q' = W cos a + n W tan a sin a, 

equal to the total compression on the segment from A to C ; 
this sum divided by bd will be the amount of compression 
on the unit of area in any cross-section in this segment. 
We also have 

P - F = (1 - n) W sin a, 

for the force perpendicular to the axis of the beam. Its 
moment for any section, at the distance, x, measured on the 
line A B, will be &-uZ^^ A **"-£■<?* 
(1 — n) W sin a x x. 



186 CIVIL ENGINEERING. 

Substituting this in the expression for R', we have 
(1 — n) Wx sin a 



R' 



M* 



for the strain on the unit of area farthest from the neutral 
axis in any section produced by deflection, x being the lever 
arm. 

For the segment of the beam, B C, it is seen that the strain 
of direct compression is due to the force 

Q / = n W tan a sin a. 

Giving values to n, from to 1, we can place the force, W, 
at any point on the axis. And knowing 5, d, and W, and 
substituting them in the foregoing expressions, we obtain the 
strains on the beam. 

Let us place it at the middle point, and suppose "W and a to 
be given. 

The value of n for the middle point is -J, which substituting 
in the expressions for P, Q, etc., there obtains Ay^^, Lt^p 

Q + Q' W cos a + iJ-W tan a sin a 
U = ~ M~ ' 

for the strain of compression on the unit of cross-section ; and 
(P — P> _ jW x sin a 

for the strain due to deflection, on the unit of cross-section 
farthest from the neutral axis. Represent these by C and R', 
respectively. To determine the greatest strain on the unit of 
area in any cross-section ; first, determine R' for the particular 
section and add to the value thus found that for C, and the 
result will be the total strain on the unit, and hence the maxi- 
mum strain in that section. 

To determine the maximum strain produced by the force, 
W, upon the unit of surface of the beam ; first, find the value 
of R' for the dangerous section and then add to it the value 
of C', the result will be the maximum strain. 

Awiming limiting values for R' and C and knowing h and 
d, the corresponding value for W can be deduced. Or, as- 
suming R' and C and having W given, we can deduce values 
for b and d. 

Suppose the beam to be vertical, then a = 0, and we get 

Q = W, and Q' = 0, 



STRAINS ON FRAMES. 



187 



or the compression in B C will be zero, and on A C equal to 
W. We also have H' — 0, or there is no horizontal thrust. 

Suppose the beam horizontal, then a — 90°, and we get H.', 
■ Q, and Q', each equal to infinity. Q^ z~C 

From this it is seen that the compression on the beam and 
the horizontal thrust at the foot both decrease as a decreases, 
and the reverse. 

255. Uniformly loaded. — Suppose the beam to be uni- 
formly loaded, and let w be the load on a unit of length of 
the beam. 

We have H — \wl tan a. 

The corresponding values for P, P', Q, and Q' are easily 
obtained. 

256. Let it be required to determine the strains on a 
triangular frame, and take for example, 

A frame made of three beams connected at the ends by 
proper joints and strained by a force acting in the plane of 
their axes and at one of the angular points. 

Suppose the plane of the axes of the three beams to be ver- 
tical, and one of the sides, B C, to be horizontal, resting on 
fixed points of support at B and C. 

Disregarding the weight of the frame itself, suppose the 
straining force to be a weight suspended from or resting on 
the point A. (Fig. 72.) 
Represent by 

W, the weight acting at A, 
a, the angle BAD, 
ft " " CAD. 




Fig. 72. 



The weight, W, acts vertically downwards and is prevented 
from falling by the support at : . The pressure exerted by 
it at A is received by the inclined beams, A B, and A C, and is 
transmitted by them to the fixed points of support at B and C. 






&*> A pvw'^ 



188 CIVIL ENGINEERING:. 

The weight, W, is therefore the resultant force acting on' the 
frame, and the pressure on the inclined beams are its compo- 
nents in the directions of the axes of the beams. 

Represent by Ad the weight W, and construct the parallelo- 
gram Abed. We have from the principle of the parallelo- 
gram of forces : 

.. Wsin/3 ' Wsina 

Ab = . , , ^ and Ac = . ( t -=. (125) 
sm (a + p) sin (a + p) v } 

The strains produced by these components are compressive. 
Knowing the breadth and depth of the beams, the amount of 
strain on the unit of cross-section can be determined; or, 
assuming a limit for this strain on the unit, the values for the 
breadth and depth of the beams may be deduced. 

These components being transmitted along the axes of the 
beams to the points of support, B and C, may be resolved at 
these points into their horizontal and vertical components 
respectively. 

Doing so, it is seen that the horizontal components are 
equal to bm and en, and are equal to each other, but act in 
opposite directions. The value for these components is 

_-. sin a sin 8 ,„,*„x 

l m ~ m = yff -—---£. . . (126) 

sm(a + p) J 

Hence, they balance each other, producing a strain of ex- 
tension on the beam, B C, the amount of which on the unit of 
cross-section, or dimensions of beam to resist which, may be 
determined. The vertical components are respectively equal 
to Am and An, and act in the same direction. We have 

w sin /3 cos a _. _ sin a cos £ , Mn ^ 

Am = W . . ov , and An = W -r— — — g. (127) 

sin (a + f3y mi (a + ft) v ' 

They are resisted by the reactions at the points of support, 
which must be strong enough to sustain these vertical pres- 
sures. Adding Am to An we find their sum is equal to AY. 
It is well to observe that producing Ad to D, we have the pro- 
portion, Am : An : : C D :' B D. That is, the vertical through A 
divides the side BC into two segments proportional to the 
vertical components acting at B and C. 

257. The common roof-truss, in which A B is equal in 
length to A C, and the angle a equal to fi, is the most usual 
form of the triangular frame. 






STRAINS ON FRAMES. 189 

For this case we would have 

W 

Ah = Ac = i , bm = &W tan a, and Am = hi = iW. 

cos cC 

Ee present by 21 the length of B C, d, the length of A D, 
and A, the length of A B — A C, and substituting in the fore- 
going expression, we have 

Ab = Ac — iW -3 , and ~bm = en = i*W"-™ 

which are fully given for any assumed value for "W when 
either two of the quantities in the second members are 
known. 

If, instead of a single weight, the frame had been strained 
by a uniform load distributed over the inclined pieces A B 
and A C, we may suppose the whole load to be divided into 
two equal parts, one acting at the middle point of A B and 
the other at the middle point of A C, the discussion of which 
would have been similar to that of the previous article. 

If the frame be inverted (Fig. 73) the method of calculat- 
ing the strains will be the same. Under this supposition the 



strains in the inclined pieces will be tensile instead of com- 
pressive, and in the horizontal piece B C will be compressive 
instead of tensile, the expression for the intensities remaining 
the same. 

258. The jib-crane. — The machine known as the jib- 
crane, which is used for raising and lowering weights, is an 
example of a triangular frame. Its principal parts are 
a vertical post, B C ; a strut, A C ; and an arm or tie-bar, A B. 
(Fig. 74.) 

Ordinarily, the whole frame allows a motion of rotation 
around the vertical axis, B C. 



190 



CIVIL ENGINEERING. 



The weight, W, suspended from the frame at A is kept 
from falling by resistances acting in the directions A B and 
A C. There being an equilibrium of forces at A, the resultant, 
W, and the direction of the resistances being known, the in- 
tensities of these resistances are easily determined. 



B^r 



A .," 




Fig. 74. 






Eepresent W by kd, and construct the parallelogram kbdc. 
kb and kc will represent the intensities of the forces acting to 
keep W from falling. 

From the parallelogram we have 



kc = W 



sin (3 



sin (a + /3)> 



(128) 



which, as it is seen, produces compression on the strut A C, 
and a transverse shearing strain at C on the part B C. Its 
horizontal component divided by the area of cross- section of 
the part B C, gives the shearing strain on the unit of cross- 
section. 

sin a 
We have also kb = W -. — ; — r—x. , 

am (a + p) 

for the strain acting in the direction of A B, which tends to 
elongate it, and to produce a cross strain on B C. The great- 
est bending moment is at C. Knowing the strains, it is a 
simple problem to proportion the pieces so that the crane may 
be able to lift a given weight, or to determine the greatest 
weight which a given crane may lift with safety. 



TRIANGULAR BRACING. 



191 



COMBINED TRIANGULAR FRAMES. 



259. Open-built beams constructed by connecting the upper 
and lower pieces by diagonal braces are examples of com- 
binations of triangular frames. 



TRIANGULAR BRACING. 

260. Triangular bracing with load at free end. — Take 
a beam of this kind and suppose it placed in a horizontal 
position, one end firmly fixed, the other free to move and 
strained by a force acting at the free end. Suppose the tri- 
angles formed by the braces to be equilateral (Fig. 75) and 
disregard the weight of the beam. 




Fig. 75. 



Represent by W the force acting at the free end A and in 
the plane of the axes of the pieces of the frame. 

The weight W acting at A is supported bj the pieces A B 
and A A', and produces a strain of compression in A A 7 and 
tension in A B. Laying off on A W the distance Ad to represent 
"W", and constructing the parallelogram Abed, we have Ac and 
Ab representing the intensities of these strains. 

From the parallelogram there results 

W 

Ac = , and Ab = W tan a. 

cos a' 

The compressive force Ac is transmitted to A' and there 
supported by the pieces A'B and A'B'. Resolving this force 
at A' into its components acting in the directions of A'B and 
A'B 7 , we have A'd' — 2W tan a, which produces compression 

w 

in A'B 7 , and A'b' = - — , which produces tension in A'B. 



cos a 
This tension A'B' is transmitted 



by the brace to B. Re- 



192 CIVIL ENGINEERING. 

solving it into its components in the directions B B' and B C, 
we have 

W 

Compression on BB'= , and 

r ?os a 

Tension on B C == 2W tan a. 

The tension at A is transmitted through the beam to B, 
hence the tension at B is equal to the sum of them, or 

Tension at B = 2W tan a -f W tan a == 3W tan a. 

Continuing this process, we find that the weight, W, strains 
all the diagonals equally, but by forces which are alternately 
compressive and tensile, and the expression for which is 

W 

. In this case the braces numbered odd in the figure are 

cos a n 

compressed, and those even are extended. 

The strains on the upper and lower beams are cumulative, 
receiving equal increments, each equal to 2W tan a, at each 
point of junction of the brace with the beam. Hence, in this 
case, for the upper beam we have 

W tan a for A B, 3W tan a for B C, 5W tan a for C D, etc., 
and for the lower, 
2W tan a for A'B', 4W tan a for B'C, 6W tan a for CD', etc. 

Having determined the strains on the different parts of 
the frame produced by a weight, W, it is easy to find the 
greatest weight that such a frame will support, or to propor- 
tion its different parts to resist the strains produced by a given 
load. 

The triangles taken were equilateral. If we denote by d 
the altitude E'x of one of these triangles, or depth of the 
beam ; by Z, the length of one of the sides F E, or distance 
between the vertices of two adjacent triangles, which we will 
call a bay ; and express the values of cos a and tan a in terms 

of these ; then we have cos a = , , and tan a = ^--.. Substituting 
which in the foregoing expressions, there obtains -r"W for the 

strains on the diagonal, and-rW for the increment to be 

added at each point of junction. 

To find the strain on any segment ; as, for example, E F. 

The tension on A B is W tan a = qjW", to which add four 



TRIANGULAR BRACING. 193 

equal increments, there being four bays between A and the 
segment E F, and we have, for the strain of tension on E F, 

* 91 

9W tan a, or its equal ^W. 

261. Triangular Bracing Strained by a Uniform Load. 

— Suppose the strains on the same beam to be caused by a 
weight uniformly distributed over either the upper or lower 
beam of the frame. 

Let AE FA' (Fig 76) be 'an open- built beam supporting a 
load uniformly distributed over the upper beam A E. 

Demote by w the weight distributed over any one segment. 

We may, without material error, suppose the whole load 
divided into a number of equal parts, each equal to that rest- 
ing on the adjacent half segments, acting at the points A, B, C, 
etc., where the braces are connected with the beam, A E. 




Fig. 76. 

Since there are four of these bays, the total load is 4:W, the 
action of which may be considered to be the same as that 
produced by the weight w acting at each of the points B, C, 
and D, and %w at A and E. 

The strains on A B, A A', A'B, and A'B' are due to the weight 

^ acting at A, and are determined as in the preceding case. 

The strains on B C, B B', B'C, and B'C are due to the ac- 
tion of the weight w acting at B, increased by the strains due 

w 
to -~- acting at A. 

The strains on the remaining parts are due to the weight 
acting at each vertex, increased by those transmitted from the 
points to the right of them. 

Hence it is seen that the strains on each of the pieces in 
any pair of diagonals are equal in amount, but different in 
kind, and increase as they go from the point of application to 
the points of support for each set. And, that the strains on 
the segments of the upper and lower beams increase in the 
same direction, the rate of which can be easily determined. 
13 



194 CIVIL ENGINEERING. 



METHOD OF MOMENTS. 

262. The strains on the different pieces may be obtained 
by using the principle of moments, or, as it is frequently 
called, the " method of sections." This method consists in 
supposing the frame divided by a section cutting not more 
than three pieces. Then taking the intersection of two of 
these pieces as a centre of moments, we must have for equili- 
brium the moment of the strain in *the third piece, with refer- 
ence to this point, equal to the sum of the moments of all the 
external forces to the right or left of this section with refer- 
ence to the same point. 

Let it be required to find by this method the strain on the 
segment E F (Fig. 75). 

If we suppose the upper beam cut in two at x by a plane 
surface, that portion of the frame to the right of E'x tends to 
turn around E'. The moment of the force producing this is 
W x km. This tendency to rotation around this point before 
separation is opposed by the resistances to tension offered by 
the fibres in this segment, the resultant of which is re- 
garded as horizontal and coinciding with the axis of the upper 
beam. 

Let T / be the resultant or sum of the tensile resistances 
brought into play in the cross-section at x. T' x E'x will be 
its moment with respect to E'. Since there is an equilibrium, 
we have 

T x E'x = W x Aaj, or 

T , x^=Wx4|/; hence 

T' = 4J -7-W, the same value before deduced. 

This method, in man} 7 cases, is the more convenient one 
for determining the amount of strain on the parts of a frame, 
and its use is simply a matter of choice. Its use is recom- 
mended as a cheek on the calculations made by the other 
method. 



VERTICAL AND DIAGONAL BRACING. 

203. Suppose the triangles, instead of being equilateral, to 
be right-angled, as in Fig. 77, and the beam strained by a 
Load, W, as in the preceding case. 

The strains on the upper and lower beams would be re- 



VERTICAL AND DIAGONAL BRACING. 



195 



spectively tensile and compressive, and cumulative as in the 
preceding case. 





F 


E D ( 


5 


3 


A 












/ a\ 


1 










i' 




E' I 


)' c 


V B' > 


W 



Fig. 77. 



The expression for the equal increment would be 

W tan a. 

The force acting on the diagonals would be compressive 
and equal to 



W 



, same as in preceding case. 



cos a 

The strain on the verticals would be tensile and equal to 
W for each. 

Representing by 

h, the length of a diagonal, A A', 

I, the length of a segment, A B, 

d, the length of a vertical, A'B, we can write 

"W" tan a = W -r, and 



W 



cos ad d ; 



(129) 



expressions more frequently used than those involving the 
circular functions when calculating the strains. 

If, in the preceding cases, W had acted in the opposite di- 
rection, that is, pushed the point A upward instead of pulling 
it down, or the same thing, the frame had been turned over 
so that the upper beam became the lower, the strains would 
have been determined in the same manner with similar 
results, excepting that the inclined pieces would have been 
extended instead of compressed, and the verticals compressed 
instead of extended. 



196 



CIVIL ENGINEERING. 



ANGLE OF ECONOMY. 






264. Let it be required to determine the angle which the 
braces should make with each other so that with the minimum 
amount of material in them the most useful effect may be 
produced. 

All things being equal, the efficiency of a brace increases 
with the amount of strain it resists successfully, and with the 
horizontal distance between its extremities. Its volume is a 
direct function of its length and cross-section. 

Take a triangular frame, the inclined sides of which are 
equal in length and of uniform cross-section ; the weight to 
be supported and the distance between the points of support 
being given. 

It is required to find the angle that the inclined sides shoidd 
make with each other so that the volume of material in them 
shall be a minimum. 

Denote by (Fig. 78) 

A, the length of A B = A C, 

21, the length of B C, 

d, the length of A D, and 

2 k), the weight to be supported at A. 

The strain on A B is equal to W--T-. 




Fig. 78. 



From this expression it is seen that, W being constant, the 
strain on the brace varies directly with h and inversely wirli 
d. Assuming a particular value for h, the strain increases as 
d decreases ; and the converse. The strain on the braces in 
this case is one of compression. Suppose the resistance 



ANGLE OF ECONOMY. 197 

offered to this strain by the brace to vary directly as the cross- 
section, and represent the cross-section by h 2 . Let C be the 
limit of strain allowed upon the unit of cross-section for the 
material of which it is composed. We can then write the 
following equation : 

W^-= ¥ x C, . . . . (130) 

from which we obtain 

» w h 

and 

W h 2 
h 2 h = -pT x ;7> ^ or tne volume of the brace. 

Substituting d 2 + P in this expression for h 2 , we have 

Volume or brace = ^ x — j — . . (131) 

The value of d = I makes this function a minimum. Hence, 
the angle made by the brace with the perpendicular A D let 
fall from A on the side B C is equal to 45°, and that between 
the braces, 90°. 

If the frame be turned over and the weight suspended from 
the vertex A, the discussion would remain the same, only that 
the braces would become ties instead of struts. 

The resistance to tension in a tie varies directly with the 
area of cross-section, however long the piece may be, and 
therefore the angle above obtained is the true angle of econ- 
omy in all cases for ties. This is not the case for struts, for 
experiment lias shown (Art. 202) that when the diameter is 
small in comparison to its length, the resistance to compres- 
sion becomes also a function of its length, which latter must 
be duly considered. 

The angle of economy for a strut when its length exceeds 
its diameter more than fifteen or thirty times can be deter- 
mined by taking the formulas deduced from Hodgkinson's 
experiments for finding the strength of pillars, and following 
the steps just described. 

Merrill, in his " Iron Truss Bridges," gives the angle of 
economy for a cast-iron strut in a triangular frame at 27° 51', 
or the depth of the frame to be a little greater than one-fourth 
of the span. In diagonal bracing with vertical ties (Art. 263) 
he gives the angle of economy for the struts to be 39° 49' 
with the vertical. 



PART IV. 



CHAPTEE IX. 

MASONRY. 

265. Masonry is the art of erecting structures in stone, 
brick, and mortar. 

It is classified, from the nature of the material used, into 
stone, brick, and mixed masonry ; from the manner in which 
the material is prepared, into cutstone, ashlar, rubble, and 
hammered masonry; and from the mode of laying the 
blocks, into irregular and regular masonry. 



MASONRY STRUCTURES. 

266. Masonry structures are divided into classes accord- 
ing to the kind of strains they are to sustain. Their forms 
and dimensions are determined by the amount and kind of 
strains they are required to resist. They may be classed as 
follows : 

1st. Those which sustain only their own weight; as walls 
of enclosures. 

2d. Those which, besides their own weight, are required to 
support a vertical pressure arising from a weight placed upon 
them ; as the walls of a building, piers of arches, etc. 

3d. Those which, besides their own weight, are required to 
resist a lateral thrust ; as a wall supporting an embankment, 
reservoir walls, etc. 

4th. Those which, sustaining a vertical pressure, are sub- 
jected to a transverse strain ; as lintels, areas, etc. 

5th. Those which are required to transmit the pressure they 
directly receive to lateral points of support; as arches. 



RETAINING WALLS. 199 



WALLS. 

267. Definitions. — In a wall of masonry the front is called 
the face ; the inside or side opposite, the back; the layer of 
stones which forms the front is called the facing, and that of 
the back, the backing ; the portion between these, forming 
the interior of the wall, the filling. 

If a uniform slope is given to the face or back, this slope is 
termed the batter. 

The section made by a vertical plane passed perpendicular 
to the base of the wall is called the profile. 

Each horizontal layer of stone in the wall is called! a course ; 
the upper surface of the stone in each course, the bed or 
build; and the surfaces of contact of two adjacent stones, 
the joints. 

When the stones of each layer are of equal thickness 
throughout, the term regular coursing is applied ; if un- 
equal, irregular or random coursing. The particular ar- 
rangement of the different stones of each course, or of con- 
tiguous courses, is called the bond. 

Walls.— The simplest forms of walls are those generally 
used to form an inclosing fence around a given area, or to 
form the upright inclosing parts of a building or room. 



RETAINING WALLS. 

268. A retaining "wall is the term used to designate a 
wall built to support a mass of earth in a vertical position, or 
one nearly so. The term sustaining is sometimes applied to 
the same case. In military engineering, the term revetment 
wall is frequently used to designate the same structure. 

The earth sustained by a retaining wall is usually deposited 
behind it and against the back after the wall is built. If the 
wall is built against the earth in its undisturbed position, as 
the side of an excavation or cutting, it is called a face-wall, 
and sometimes breast-wall. 

Reservoir "walls and dams are special cases of retaining 
walls, where, instead of earth, water is the material to be sup- 
ported. 

Counterforts are projections from the back of a retaining 
wall for the purpose of adding to its strength. The projec- 
tions from the face or the side opposite to the thrust are 
called buttresses. 



200 



CIVIL ENGINEERING. 



AREAS, LINTELS, AND PLATE-BANDS. 

269. The term area is applied to a mass of masonry, usually 
of uniform thickness, laid over the ground enclosed by the 
foundations of walls. 

The term lintel is applied to a single stone, spanning an 
interval in a wall ; as over the opening for a window, door, etc. 

The term plate-band is applied to the lintel when it is 
composed of several pieces. The pieces have the form of 
truncated wedges, and the whole combination possesses the 
outward appearance of an arch whose under surface is plane 
instead of being curved. 



ARCHES. • 

270. An arch is a combination of wedge-shaped blocks, 
called voussoirs or arch-stones, supporting each other by 
their mutual pressures, the combination being supported at 
the two ends. (Fig. 79.) 

These blocks are truncated towards the angle of the wedges 
by a curved surface, generally normal to the joints between 
the blocks. 

The supports against which the extreme voussoirs rest are 
generally built of masonry. 



F 












n 








A 


H 


B 








WW////M 


W////////S 


WW///////M 


WMmmmmmmm 


W%MM> 


WtiZM 


:/ 


' 



Fig. 79. 



If this mass of masonry or other material supports two 
successive arches it is called a pier; if the pier be strong 
enough to withstand the thrust arising from either of the 
arches alone, it is called an abutment pier; the extreme 



ARCHES 201 

piers which support on one side an embankment, generally ol 
earth, and on the other an arch, are called abutments. 

The under surface of the arch is called the intrados or 
soffit. The exterior surface is termed the extrados or back. 
The sides of the arch are called reins or haunches. The 
highest Hue of the soffit, that projected at C, is called the 
crown, hence the term crown is sometimes applied to the 
upper portion of the arch. The highest voussoir, the one at 
C, is called the keystone of the arch. 

The connection of the arch with the pier is called the 
impost. If the top surface of an abutment or pier is sloped 
to receive the end of the arch, this surface is called a skew- 
back. The line at which the soffit of the arch begins, or 
springs from its piers, is called the springing line. The 
stones on which the springing lines rest are called the cushion 
stones. When the arch is terminated by plane surfaces, 
these are called the heads of the arch. The axis of the sur- 
face forming the soffit is the axis of the arch. 

The chore! , A B, of the head, is termed the span, and the 
height, H C, of the keystone above this line, is termed the 
rise. The length of' the arch is that of the springing line. 
The courses of stones parallel to the head of the arch are 
called ring-courses. The courses which run lengthwise of 
the arch are termed string-courses. The joint-s between the 
stones of the ring- courses are called heading joints. Those 
betweeu the stones of the string -courses are termed coursing 
or bed-joints. 

A wall standing on an arch and parallel to the head is 
called a spandrel- wall. 

271. Classification. — Arches are classified from the direc- 
tion of the axis with respect to a vertical or horizontal plane, 
oi* from the form of the soffit. 

A right arch is one whose axis is perpendicular to the 
heads. The arch is called oblique or askew, when the axis 
is oblique to the heads ; and rampant, when the axis is 
obliq^to the horizontal plane. 

Arches are termed cylindrical, conical, -warped, etc., ac- 
cording as the soffit is cylindrical, conical, etc. 

272. The cylindrical arch. — The cylindrical is the most 
usual and the simplest form of the arch. A section taken at 
right angles to the axis is called a right section. 

These arches are classified according to the shape of the 
curve cut out of the soffit by the plane of right section. 

If the curve be a semi-circle, the arch is called a full, 
centre arch ; if less than a semicircle a segmental arch. 



202 



CIVIL ENGINEERING. 



When the section gives a semi-ellipse, the arch is called an 
elliptical arch ; if the curve resembles a semi-ellipse, but is 
composed of arcs of circles tangent to each other, the term 
oval of three, five, etc., centres, according to the number of 
arcs used, is applied to designate it. 

273. Groined and Cloistered Arches. — The intersection 
of cylindrical arches having their axes in the same plane, and 
having the same rise, form the arches known as groined and 
cloistered. 

The groined arch (Fig. 80) is made by removing from 
each cylindrical arch those portions of itself which lie with- 
in the corresponding parts of the other arch ; in this way, 
the two soffits are so connected that the two arches open 
freely into each other. 







Fig. 80 — Represents the plan of the soffit and the right sections M and 

N of the cylinders forming a groined arch. 
aa, pillars supporting the arch. 
be, groins of the soffit. 
om, mn, edges of coursing joint. 

A, key- stone of the two arches formed of one block. 

B, B, groin stones, each of one piece, situated below the key-stone, and 
forming a part of each arch. 



The curves of intersection of the soffits form the edges of 
salient angles and are termed groins, hence the name of the 
arch. 

The cloistered arch (Fig. SI) is made by retaining in ouch 
cylindrical arch only those portions of itself which lie within 
the corresponding portions of the other arch ; thus, a portion 



ARCHES. 



203 



of the soffit of each arch is enclosed within the other, these 
portions forming a four-sided vaulted ceiling. 



Fig. 81 — Represents a horizontal section 
through the walls supporting the arch and 
plan of the soffit of a cloistered arch. 

B, B, the walls of the enclosure or abut- 
ments of the arches. 

ab, curves of intersection of the soffits. 

c, c, groin stones. 




This arch was much used in forming the ceilings of the 
cells of monasteries; from their object and use is derived the 
term cloistered. 

274. Annular arches. — An annular arch is one that may 
be generated by revolving the right section of an arch about 
a line lying in the plane of the section, but not intersect- 




Fig. 82. — N, right section of an annular arch. 
C, plan of soffit. 



ing it. This line is usually vertical and also perpendicular 
to the span of the arch. (Fig. 82.) The axis is curved 



204 



CIVIL ENGINEEEING. 



being described by the centre of the curve of right section. 
The coursing joints are conical, and the heading joints are 
plane surfaces. 

275. Domes. — An arch whose soffit is the surface of a 
hemisphere, the half of a spheroid, or other similar surface, 
is called a dome. The soffit may be generated by revolving 
the curve of right section about the rise for 360°, or about 
the span for 180°. In the first case the horizontal section at 
the springing lines is a circle, in the other it is the generating 
curve. 

The plan may be any regular figure. Fig. 83 represents a 
plan and vertical section of an octagonal dome, 




FlG. 83. — A, vertical section of octogonal dome. 

B, B, horizontal section and plan of soffit. 

276. Conical arches. — Their name explains their con- 
struction. They are but rarely used, in consequence of the 
varying sizes of the voussoirs. 

277. Arches with warped soffits. — Arches, whose 
soffits are warped surfaces, are frequently used. The partic- 
ular kind of warped surface will depend upon circumstances. 

A common example of this class is an arch which has the 
same rise at the heads but unequal spans. The soffit in this 
ease may be generated by moving a straight line so as to con- 
tinually touch the curves of section of the soffit at the heads, 
and at the same time to remain parallel to the plane of the 
springing lines. A surface generated in this manner belongs 
to the class of warped surfaces having a plane director, in 
particular cases it is a conoid, hence the name of conoidal 
arches is frequently applied to this kind. 



DISTRIBUTION OF PRESSURE. 



205 



Arches whose soffits may be thus generated possess the 
advantage of having straight lines for the edges of the joints 



t lengthwise in the soffit. 



278. Oblique or askew arches- — An arch whose axis 
makes an angle with the head is called oblique or askew. 
In arches of this kind the chord of the arc of the head is the 
span. The angle of obliquity is the angle which the axis 
makes with a normal to the head. 



MECHANICS OF MASONRY. 



DISTRIBUTION OF PRESSURE. 

279. The base of a structure supports the weight of the 
structure and the pressure arising from the load placed upon 
the structure or from the thrust which the structure is re- 
quired to resist. 

For stability, it is necessary that the resultant pressure 
should intersect the base within the polygonal figure formed 
by its sides, and that the forces acting within the base be 
compressive. 

The point in which the resultant pierces the plane of the 
base is called the centre of pressure. 

It is necessary .to know what the pressure upon the differ- 
ent points within the base may be, and to determine the 
limits of deviation of the centre of pressure from the centre 
of figure of the base. 

Suppose the resultant pressure to be normal to the plane 
of the base. 

280. Normal pressure. — Suppose a series of blocks, rect- 
angular parallelopipedons in form with equal bases, but 
(Fig. 84), whose altitudes in- 
crease in arithmetical progres- 
sion, be placed side by side on a 
given plane area, A B C D. It is 
evident that the pressure on the 
area, A B C D, is less for that part 
under block 1, than it is for the 
part under block 5, and that the 
pressure on any part of A B C D 
will be directly proportional to 
the altitude of the Block resting 
upon it. 

If these blocks be very thin, 
that is, the width of the bases 
measured in the direction of A B be infinitely small, 




CIVIL ENGINEEEING. 



the minimum altitude being A E and the greatest being B F, 
the ordinates of the trapezoid, A E F B, may then be taken 
to represent the pressures upon the area, A B C D. And 
since this line, EF, passes through the middle point of the 
upper side of the end of each block, the total pressure on 
A B C D by the blocks, 1, 2, 3, 4, and 5, is equal to the total 
pressure shown by the trapezoid, A E F B. The resultant of 
the pressures represented by this trapezoid will pass through 
its centre of gravity. 

Hence, a uniformly varying pressure acting on a rectangu- 
lar base may be represented by the area of a trapezoid, the 
centre of pressure lying vertically under the centre of gravity 
of the trapezoid. 

281. Uniformly distributed pressure. — If the blocks 
were all of the same size and of the same material, the pres- 





Fig. 85. 



Fig. 86. 



sure on the unit of area of the* rectangle would be the same 
and the centre of pressure would coincide with the centre 
of the base. The line E F (Fig. 84) would be parallel to A B. 

The system of forces acting to produce the pressure may 
be represented in this case by a rectangular parallelopipedon 
of homogeneous density, of which the rectangle is the base. 
(Fig. 85.) 

Let A B C D be the area pressed by this system of forces, and 
P, the resultant of this system. From what precedes, P acts 



NORMAL TEESSUEE. 



207 



through the centre of gravity of the rectangle, and the 

P 
pressure on each unit of area will be -p 

282. Uniformly varying pressure. — Suppose the pressure 
to be zero along the line A D (Fig. 84), and to increase uni- 
formly toward B C, along which the pressure is equal to B F. 
The system of forces producing this pressure may be repre- 
sented by a wedge-shaped mass of homogeneous density, as 
shown in Fig 86. The trapezoid of Fig. 84 becomes a tri- 
angle in Fig. S6, and the centre of pressure is below the centre 
of gravity and to the right of the centre of base, 0, at a dis- 
tance equal to oiie-th+rd of the longest side, A B, of the base. 

The pressures on each of the lines parallel to A D vary as 
the ordinates of the triangle, N L M, and it is evident that the 

P 
pressure P at 0, the centre of the rectangle, is equal to -j-, 

the mean pressure on the surface of the rectangle. 

The pressure at X will be equal to zero, and at X' twice that 
2P 
at 0, or - ^ - * 

To find the pressure P' at any distance x from 0, measured 
on the middle line X X', we have, representing the sides of the 
rectangle by 2a and 2b, 

? : P' : : N H : N P, or a : a + x, 

whence, p/ = x(f +1 ) (132) 

293. Uniformly varying pres- 
sure combined with uniformly 
distributed pressure. — If we 

suppose the wedge-shaped mass 
of the last case placed upon the 
rectangular parallelopipedon of 
the previous case, so that the base 
of the wedge shall exactly coincide 
with the upper base of the paral- 
lelopipedon, the corresponding 
pressure upon the base may be 
represented by Fig. 87. In this 
case, the centre of pressure will 
be, as before, below the centre 
of gravity of the mass represent- 
ing the system of forces and to the 
right of the centre of base, 0, a Fig. 87. 




cfc 







208 CIVIL ENGINEEKING-. 

distance less than one-third the longest side. Represent the 
resultant pressure by P, the distance V by %', and divide the 
middle line X X' into three equal parts, and let K and K' be the 
points of division. Resolve the resultant P into two parallel 
components P x and P 2 , acting at the points K and K'. 

If P x acted alone, from what we have shown, we find the 
pressure at any point x to be 

VJx 



= m* » )■ 



in which P ; is the pressure due to Pi ; in the same way the 
pressure P" due to P 2 acting alone would be 

r-K-l+'h-Sfe- 1 )- 

The pressure P^ due to P will be equal to their sum, or 

To find the value of Pj and P 2 in terms of P, represent 
these parallel components as acting at M and M'. From the 
principle of parallel forces, we have 

%a _ /a \ , 

and 



p ' x T= Px .(l + 1 



2 a (a ,\ 

•t =Px r ? )' 



From which, finding the value of P t and P 2 , and substitut- 
ing in the expression Jor P^ we have 



P„ = 






for the pressure on the unit of area at the distance x from the 
centre of the base measured on the line XX'. 

284. Suppose the load, instead of being symmetrical with 
respect to the line X X', was symmetrical with respect to some- 
line making an angle with it. If we know the centre of 
pressure, the pressure on any unit of area of the base may be 
determined. 

Let the centre of pressure be at any point, as V in the 
rectangle, and let the co-ordinates of this point be denoted by 
x' and y' (Fig. SS). 



NORMAL PRESSURE. 



209 



Through V draw a straight line V^ V 2 , so that V shall be its 
middle point. The point* V,. would have for its abscissa 2a/, 
and V 2 for its ordinate 2y'. 




The resultant P being resolved into two parallel compo- 
nents acting at V t and V 2 , these will be each equal to -w. 

From the preceding we have the pressure at any point pro- 
duced bj a force at V\ to be 



2A\ 



1 + 



3 x 2xx' 



). 



and for that produced by the force at V 2 to be 



y 2A\ 



1 + 



3_x_2y'y 



). 



and hence the total pressure on the unit of area due to P 
acting at V, at the point whose co-ordinates are a? and y, will 
be 






3 x' x St/ ' y 



1 + — — + 

a 2 o z 



). . (135) 



The pressure at the different points of the base may be 
determined in a similar way when the base is a circle, ellipse, 
lozenge, etc. 

285. General solution. — It is evident that there is a ten- 
dency to produce rotation about some right line in its plane 
whenever the resultant pressure pierces the plane of the base 
in any point excepting the centre of figure of the base. Re- 
garding the base as a cross-section, this right line will be its 
neutral axis. 
14 



210 CIVIL ENGINEERING. 

And since the condition is imposed that all the forces 
acting within the base shall be compressive, it is evident that 
this neutral axis must remain outside of, or at least tangent to, 
the base. If it should intersect the base, it is plain that the 
portion between the neutral axis and the centre of pressure 
would be compressed, while the portion of the base on the 
other side would be subjected to a strain of extension, a con- 
dition which is not allowable. 

The centre of pressure of the base is the centre of percus- 
sion of the plane area forming the base. Hence, the general 
solution obtained from mechanics for obtaining the centres of 
percussion and axes of rotation for any plane figure may- be 
applied to these cases. 

The normal pressure upon the base is generally produced 
by a uniformly distributed load, by a uniformly varying one, 
or by a combination of the two, placed upon the structure. 
These are the cases which have been considered. 

286. Symmetrical base. — In general the blocks used in 
building have a plane of symmetry, and these loads above 
named are symmetrically distributed with respect to this 
plane and to the base of the block. It follows, therefore, 
that the resultant pressure pierces the base in its axis or- 
middle line. 

For such cases the expression for the pressure on any point 
will be of the general form, 



P- = 



P U . K 
A 



(1 + *?), . . . (136) 



in which K is a positive coefficient depending upon the figure 
of the base. We have found it equal to 3 for the rectangle ; 
we would find it equal to 4 for the ellipse or circle, and 6 for 
the lozenge, 2a being the longest diameter. Hence we con- 
clude that the pressure is more equally distributed over a rect- 
angular base than over a circular, elliptical, or lozenge-shaped 
one. 

In the general expression for P^ it is seen that in the 
rectangle if x' is greater numerically than ± Ja, that the 
corresponding values of x = ^fa give negative values for P^. 
That is, there will be no pressure on the opposite edge ; on 
the contrary, there will be tension, and the joint will open or 
tend to open, along this line. If x' = ± \a the values of P a 
for x — ± a are 0; that is, there is no pressure on the edge. 
Hence, if the pressure is to be distributed over the entire 
base, the resultant must pierce it within the limits of ± J^*« 

287. Oblique pressure. — In a large number of eases, 






STRAINS ON MASONRY. 211 

especially in structures of the third and fifth classes, the 
resultant pressure has its direction oblique to the plane of 
the base. 

This resultant may be resolved at the centre of pressure 
into two components, one normal to the plane of the base 
and the other parallel to it. The former is the amount of 
force producing pressure on the base, and is to be considered 
as in the preceding cases. The* latter does not produce pres- 
sure, but acts to slide the base along in a direction parallel to 
its plane. The effect of sliding will be alluded to in future 
articles. 



MASONRY STRUCTURES OF THE FIRST AND SECOND CLASSES. 

288. The strains which these structures sustain are pro- 
duced by vertical forces. 

For stability, the resultant pressure should pierce the plane 
of the base at a distance from the middle point of the base of 
any vertical section not greater than one-sixth the thickness of 
the wall at its base. 

The wall having to support a load, either its own weight 
alone, or its weight with a load placed upon it, the largest 
stones should be placed in the lower courses, and all the 
courses so arranged that they shall be perpendicular, or as 
nearly so as practicable, to the vertical forces acting on the 
wall. Great care should be taken to avoid the use of con- 
tinuous vertical joints. 

The thickness t»f the wall will depend upon the load it has 
to support and the manner of its construction. 



STRUCTURES OF THE THIRD CLASS. 

289. Retaining walls, besides supporting their own 
weight, are required to resist a lateral thrust which tends to 
turn them over. 

Observation has shown that if we were to remove a wall 
or other obstacle supporting a mass of earth against any one 
of its faces, a portion of the embankment would tumble down, 
separating from the rest along a surface as B R (Fig. 89), 
which may be considered a plane ; and that later more and 
more of the earth would fall, until finally a permanent slope 
as B S is reached. 

The line B R is called the line of rupture, the line B S 



212 



CIVIL ENGINEERING. 



the natural slope, and the angle made by the natural slope 
with the horizontal is termed the angle of repose. The 
angle C B R is called the angle of rupture. If dry sand be 
poured out of a vessel with a spout upon a flat surface, the 
sand will form a conical heap, the sides of which will make 



D 




C R S 


A 


$: 


w 



Fig. 



a particular angle with the horizontal, and it will be found 
that the steepness of this slope cannot be increased, however 
judiciously the sand may be poured, or however carefully it 
is heaped up. This slope or angle of repose varies for differ- 
ent earths, being as much as 55° for heavy, clayey earth, and 
as little as 20° for fine dry sand. 

This prism of earth C B R, which would tumble down if 
not sustained, presses against the wall, producing a horizontal 
thrust, and the wall should be made strong enough to resist 
it. 

290. Two distinct problems are presented : the first being 
to ascertain the intensity of the thrust exerted against the wall 
by the earth ; and the second, to determine the dimensions 
of a wall of given form so as to successfully resist this thrust. 

The intensity of the thrust depends upon the height of the 
prism, and upon the angle of rupture. 

The angle of rupture, or the tendency in the earth to slip, 
is not only different for the various kinds of earth, but is 
different in the same earth, according as it is dry or saturated 
with water, being greater in the latter case. 

The manner in which the earth is filled in, behind the wall, 
affects the intensity of the thrust, the latter being less when 
the earth is well rammed in layers inclining from the wall 
than when the layers slope towards it. 

Therefore, in calculating the amount of resistance the wall 
should have, the effect produced by the maximum prism of 
pressure under the most unfavorable circumstances should be 



1 



RETAINING WALLS. 213 

considered. The greatest pressure that earth can produce 
against the back of the wall is when the friction between its 
grains are destroyed, or when the earth assumes the form of 
mud. The pressure under these circumstances would be the 
same as that produced by a fluid whose specific gravity was 
the same as earth. 

291. Retaining walls may yield by sliding along the base 
or one of, the horizontal joints ; by bulging ; or by rotation 
around the exterior edge of one of the horizontal joints. 

If the wall be well built and strong enough to prevent its 
being overturned, it will be strong enough to resist yielding 
by the other modes. 

Hence, the formulas used in determining the thickness of a 
retaining wall are deduced under the supposition that the only 
danger to be feared is that of being overturned. 

Having determined the horizontal thrust of the prism of 
pressure, its moment in reference to any assumed axis can be 
obtained. 

A wall to be stable must have the moment of its weight 
about the axis of rotation greater than the moment of the 
overturning force about the same line. 

The term stability in this subject differs slightly in its 
meaning from that previously given it. A mass is here said 
to be stable when it resists without sensible change of form 
the action of the external forces to which it is exposed — the 
variations produced by these forces being in the reactions of 
the points of support and the molecular forces of the body, 
and not changing in any way the form of the mass. 

The excess of moment in the wall, or factor of safety, as 
we have heretofore designated it, will vary in almost every 
special case, being much greater for a wall exposed to shocks 
than when it has to sustain a quiescent mass ; greater for a 
wall poorly built, or of indifferent materials, than one of bet- 
ter material and well constructed. The formulas which are 
used give results which make this factor of safety at least 
equal to 2, or twice as strong as strict equilibrium requires. 



'with back parallel to the face. 

292. Let it be required, to find the thickness of a retaining 
wall, the upper surface of the embankment being horizontal 
and on a level with the top of the wall. The wall being of 
uniform thickness, with vertical face and back. 



214 



CIVIL ENGINEERING. 



Denote by (Fig. 90), 

H, the height B C of the wall, 
b, " thickness A B of the wall, 
w, u weight of a unit of volume of the earth, 
w r , " " " same unit of volume of masonry, 
a, " angle C B S of the natural slope with the verti- 
cal B C, 
/3, " angle S B F of the natural slope with ,the hori- 
zontal. 
Let it be assumed that the density and cohesion of the 
earth are uniform throughout the mass. The pressure ex- 
erted against the wall may then be represented by a single 



I 




Fig. 90. 

resultant force acting through the centre of pressure on the 
surface of the wall. 

If we suppose the prism C B S to act as a solid piece, the 
friction along B S would be just sufficient to prevent sliding, 
and there would be no horizontal thrust. This is true for 
any prism making an angle less than (3. 

The horizontal thrust upon the back .of the wall must there- 
fore be due to a mass of earth, the lower surface of which 
makes a greater angle with the horizontal than ft. 

Let B R be a plane which makes an angle greater than /3, 
and represent by <£ the angle which it makes with the natural 
slope. 

We may suppose two cases : one in which there is no fric- 
tion existing between the prism and the plane which supports 
it ; and the other, in which there is friction. 

In the first case, the horizontal thrust would be equal to 
that of a fluid whose specific gravity is the same as that of 
the earth, or fu 

Hor. thrust = JwH a , 

the centre of pressure being }H below C S. 



KETAINING WALLS. 



215 



In the second case, the friction between the plane and 
prism is considered, and if we denote by P the horizontal 
component of the pressure acting to overthrow the wall, and 
neglect the adhesion and friction of the eartjp. on the back of 
the wall, we have far*** *4#**UT £c±+>y&* ^ *"-*-£< 

F = iwW\xmH> . . . (137) 

The moment of this force about the ed^e A will be 



iZu.u*#)ti-- 






U**&-if)tS*,.t* jj 



IS 



The moment of the weight of the wall about the same line 



Equating these moments, we have 






whence, 



b — HtaEr^ 



Jlw' 






(138) 



for the value of the thickness of base to give the wall to resist 
the pressure due to P. 

It can be shown that the maximum prism of pressure will 
be obtained when the angle of rupture, C B R, is equal to 
i (90° — /S), or equal to \a. This has also been proved by ex- 
periment. Substituting for <f> this value in the expression 
for b, and we get, 



H tan 



a 1 1 w 

2 V 1w' 



The value for P may be put under the form, 

1 - sin /3 



Y=hWw x 



1 + sin 



(139) 



(140) 



*■ r * '" 



which is the form in which it frequently appears in other 
works when treating this subject. 
Suppose B R to coincide with B S, then <j> = 0, and hence 

11 = 0, 

a conclusion already reached. i * m < 

' • A 
I * * ' » i 



?/ 



c 



216 



CIVIL ENGINEEELNG. 




Fig. 91. 



293. General case. — The wall was assumed vertical in 
the preceding case. The general case would be where the 

back of the wall and the up- 

&...■■■" per surface of the embank- 

^--"7 ment were both inclined to 

the horizontal. Let B C (Fig. 

91) be the back of the wall ; 

C S, the upper surface of the 

embankment ; B S, the line 

of natural slope ; and <j> and 

/3 represent the same angles 

as in preceding example. The 

pressure ou the back of the 

wall is produced by some prism as C B R. The horizontal 

thrust produced by this prism is equal to its weight multiplied 

by the tan <£, or tjW*. u«*XtZ -l^^^J^. 

P = w x area CBR x tan <f>. 

Let it be required to find the maximum prism of pressure. 
This will be a maximum when the product of the area CBR 
and the tan <£ is a maximum. 

Draw through C and R perpendiculars to the line of natural 
slope B S. Represent the distance R L by x, the distance C K 
by a, and the distance B S by b. 

The area C B R is equal to 

\ab — \xh. 
Substituting in the expression for P, we get 
P = w x i b (a — x) tan #. 
Represent the angle B S C by ft', and we can write 

P = w x \b(a — x) j —57. 

x '6 — x cot ft 

This expression is in terms of a single variable x. Taking 

/V'VJ ni& 

the factor 1 —57, and differentiating, and placing the 

— x cot p ' °' . r ° 

numerator of the differential equal to zero, we get 

{b - x cot /3') (a - 2 x) - (ax - x 2 ) ( — cot 0') = 0, 



whence 

x 2 cot /3' — 2bx=-db.. . . 

This may be put under the form 

ab — bx = bx — a? cot /3' = x (b — x cot ft') 

ab — bx — x x B L. 



(141) 



or 



RETAINING WALLS. 217 

Whence, 

area CBS — area RBS = |(«xBL) = area R B L, 
and 

area R B L = area C B R, 

or the thrust is a maximum when the area C B R is equal to 
the area B R L. 

If C S is horizontal and B C is vertical, t he line3 C K and 
R-b- eo i n r ri d e in -d kootion with G-S ,-^t*»d the triangle R B L is 
rfrr equal to R B fa-mAlie line B R bisects the angle CBS. This trv 
result is the same as that of the previous case. 

Substituting in the expression for P, the area R B L for the 
area C B R, we get 

P = w x area R B L x tan <£. 

Substituting for this area and for the tan <f>, their values in 
terms of x, we get 

Y = iwx 2 , (142) 

for the maximum thrust. t 

From equation (141) we find the value of x to be 



x = h tan /3' — V b tan /3 {b tan fi — a). 

We may write this value of x under another form by draw- 
ing from B, the line B E perpendicular to B S and repre- 
senting it by c. We have c = o tan f3' } and substituting, we 

get ' 

x — c«V g (c — a). 

Substituting this value of a? in equation (142), we get 

P = \w (c—Vc{c-a) ) 2 , . . (143) 

for the horizontal thrust, produced by the maximum prism of 
pressure. ^ ^ 

Knowing the horizontal thrust, its moment around the 
edge, A, can be obtained. The moment of the wall around 
the same line is easily found. 

Equating these moments, the value of 5 can be deduced, 
giving the requisite thickness for an equilibrium. 

294. These examples show the general method used to de- 
termine the thickness of retaining walls. 

The specific gravity of the materials forming an embank- 
ment ranges between 1.4 and 1.9, and that of masonry be- 

w 
tween 1.7 and 2.5. The ratio of the weights — , is therefore 

° w 

ordinarily between J- and 1. For common earth and ordinary 



218 



CIVIL ENGINEERING. 



W 

masonry it is usual for discussion to assume — 7 = #, and a = 

45°. In practice it is recommended to measure the natural 
slope of the earth to be used, and to weigh carefully a given 
portion of the masonry and of earth, the latter being 
thoroughly moistened. 

In military works, the upper surface of the embankment 
is generally above the top of the wall. The portion of the 
embankment above the level of the top is called the surcharge, 
and in fortifications rests partly on the top of the wall. When 
its height does not exceed that of the wall, the approximate 
thickness may be obtained by substituting, the sum of the 
heights of the wall and the surcharge, for H in the expression 
for the thickness already obtained. 

The manner in which earth acts against a wall to overturn 
it cannot be exactly determined, hence, the 



thrust not being 
exactly known, the results obtained are only approximations. 
Nevertheless, a calculation right within certain limits is better 
than a guess, and its use will prevent serious mistakes being 
made. 




In our discussion the cohesion of the particles of earth to 
each other and their friction on the back of the wall have 
been disregarded. The results therefore give a greaterthick- 
ness than is necessary for strict equilibrium, and hence errs 
on the side of stability. 

295. A.mongthe many solutions of this problem, those given 



KETAINING WALLS. 



219 



by M. Poncelet, and published in No. 13 " Du Memorial de 
l'Ofiicier du Genie/' are the most complete and satisfactory. 

In this memoir he gives a table from which the proper 
thickness of a retaining wall supporting a surcharge of earth 
may be obtained. 

The principal parts of this table giving the thickness in 
terms of the height, for surcharges whose heights vary be- 
tween and twice the height of the wall, are as follows : 

Eepresent by (Fig. 92). 

H, the height B C of the wall ; 

h, the mean height of C F of surcharge ; 

a, the angle CBS made by the vertical with line of natu- 
ral slope B S. 

/?, the angle of natural slope with the horizontal ; 

y, the coefficient of friction = cotan a ; 

u, the distance from foot of surcharge E to D outer edge 
of wall ; 

w, weight of unit of volume of earth ; 
5 weight of unit of volume of masonry. 



J* 



TABLE. 









EATIO OF HEIGHT TO THICKNESS, 


ft 

OB- 








When w = w' and 




10 = f ID' 


a 


/=0.6 

= 31° 


/=1.4 
/3 = 51° 25' 


/=1 = 45° 


fs= 0.60 = 31° 


/3 = 41° 25' 




w=0 


u=±TL 


u=Q 


u-=tK 


i/-0 


u=i*L 


u=0 


u=iH 


u=0 


u=in 





0.452 


0.452 


0.258 


0.258 


0.270 


0.270 


0.350 


0.350 


0.198 


0.198 


0.1 


0.498 


0.507 


0.282 


0.290 


0.303 


0.306 


0.393 


0.393 0.222 


0.229 


0.2 


0.548 


0.563 


0.309 


0.326 


0.336 


0.342 


0.439 


0.445 0.249 


0.262 


0.4 


0.665 


0.670 


0.369 


0.394 


0.399 


0.405 


0.532 


0.522 0.303 


0.299 


0.6 


0.778 


0.754 


0.436 


0.450 


0.477 


0.457 


0.617 


0.572 


0.360 


0.328 


0.8 


0.867 


0.820 


0.510 


0.501 


0.544 


0.504 


0.668 


0.610 I 0.413 


0.357 


1 


0.930 


0.873 


0.571 


0.546 


0.605 


0.540 


0.707 


0.636 0.457 


0.384 


2 


1.107 


1.004 


0.812 


0.714 


0.795 


0.655 0.811 


0.705 i 0.622 


0.475 



220 



CIVIL ENGINEERING. 



The thickness obtained by using this table are nearly 
double that of strict equilibrium. This factor of safety or 
excess of stability is that used by Yauban in his retaining 
walls which have stood the test of more than a century with 
safety. 

The formula, 

b = 0.845 (H 4- h) a/™ x tan (45° - £), . (144) 

will give very nearly the same values as those given in the 
table. 

retaining walls, face and back not parallel. 

296. The usual form of cross-section of a retaining wall is 
trapezoidal. 

To transform a wall of rectangular cross-section, whose 
dimensions have been deduced from the rules already given 
into one of equal stability having a batter on its face, this 
batter not exceeding jf } we may use the following formula 
of M. Foncelet. / 

Let V (Fig. 93) be the base A B of the wall with trapezoidal 
cross-section. 
h, the thickness B d of wall of rectangular cross-section de- 
termined by the rule; 

n, the quotient — -^; 
B r 

H, the height B C of the wall. 

B F equal to \ of the height H. 




Fig. 93. 



The formula is as follows : 

I>' = b + T \nll. . . . (145) 



COUNTERFORTS. 221 

That is, the thickness of the equivalent traj)ezoidal wall at 
the base is equal to the thickness of the rectangular wall in- 
creased by one-tenth of the product obtained by multiplying 
the height of the wall by the quotient resulting from dividing 
the base of the slope by its perpendicular. This rule gives 
the thickness to within jfo of the true distance. If the 
distance B F be taken at one-tenth of the height, the error 
made will be very slight. 

297. Counterforts. — Counterforts are considered to give 
additional strength to the wall by dividing it into shorter 
lengths, these short lengths being less liable than longer ones 
to yield by bulging out or sliding along the horizontal courses ; 
by the pressure being received on the back of the counterfort 
instead of on the corresponding portion of the wall, thus 
increasing the stability of the wall against overturning at 
those points; and by the filling being confined between the 
sides of the counterforts, the particles of the filling, especially 
in case of sandy material when confined laterally, becoming 
packed and thus relieving the back of the wall. 

Counterforts are, ,,h^w-ev-6r, of doubtful efficiency, as they 
increase the stability of the wall but slightly against rotation, 
and not at all against sliding. They certainly should not be 
used in treacherous foundations on account of the danger of 
unequal settling. 

The moment of stability of a wall w T ith counterforts may 
be found with sufficient accuracy for all practical purposes 
by adding together the moments of stability of one of the 
parts between two counterforts, and one of the parts aug- 
mented by a counterfort, and dividing this sum by the total 
length of the two parts. 

Their horizontal section may be either rectangular or 
trapezoidal. The rectangular form gives greater stability 
against rotation, and costs less in construction ; the trape- 
zoidal form gives a connection between the wall and coun- 
terfort broader and therefore firmer than the rectangu- 
lar, a point of some consideration where, from the char- 
acter of the materials, the strength of this connection must 
mainly depend upon the strength of the mortar used for the 
masonry. 

298. Counterforts have been used by military engineers 
chiefly for the retaining walls of fortifications. In regu- 
lating their form and dimensions, the practice of Yauban 
has been generally followed ; this is to make the horizontal 
section of the counterfort trapezoidal, to make the length, ef\ 
of the counterfort (Fig. 94) equal to two-tenths of the height 



222 



CIVIL ENGINEERING. 









■of the wall added to two feet, the front, ah, one-tenth of the 
height added to two feet, and the back, cd, equal to two- 
thirds of the front, ah. 




Fig. 94 — Represents a section A and plan D of a 
wall, and an elevation B and plan E of a trape- 
zoidal counterfort. 



RESERVOIR WALLS AND DAMS. 

299. These are retaining walls which are used to resist the 
pressure of a volume of water instead of earth, and they do not 
differ mathematically from the walls already discussed. Their 
•dimensions are therefore obtained in the same way. 

Their cross-section is generally trapezoidal. 

Let A B C D (Fig 95) represent the cross-section of a reser- 
voir wall, with a vertical water face B C, and let the upper 
surface of the water be at E F. 

Represent by 

A, the depth E B of the water ; 

h' ', the height B C of the wall ; 

b, b', the upper and lower bases A B and D C ; 

w, the weight of unit of volume of water ; 

w\ the weight of unit of volume of masonrv. 

Lay off B H equal to one-third of B E, and draw the hori- 
zontal II. This gives the direction and point of application 
of the thrust on the wall produced by the pressure of the 
water. Its intensities equal to -^iv/i 2 . The weight of the wall 
acts through the centre of gravity G, and is equal to \w'h' 
(b + b'\ flic moments around the edge at A can be deter- 
mined and the values for b and // found. 



vf* 



+M- 



RESERVOIR. WALLS. 



223 



The resultant E of these pressures intersects the base A B 
between A and B. Stability requires that this should be so. 




R V- 1 P 



Fig. 95. 



If the resistance to a crushing force were infinitely great in 
the blocks forming the wall, it would make no difference 
how near the resultant came to the edge A. But as such is 
not the case, it should not come so near the edge as to pro- 
duce a pressure along the latter sufficiently intense to injure 
the material. 

The nearer the intersection is to the middle point of the 
base, the more nearly will the pressure on the foundation of 
the wall be uniformly distributed over it. 

It is evident, from the figure, that the batter given to the 
face A D contributes greatly to the uniform distribution of the 
pressure. And it is easily seen that if a -batter had been given 
to_tl4©-wafeer"face-ftGd the outer face had been made vertical, 
the resultant would have intersected the base much nearer to 
the edge A, producing a far greater pressure in that vicinity 
than in the former case. 




Fig. 9G. 

300. Reservoir walls are usually constructed with both their 
faces sloped. Having found the thickness of the wall, as 



<1 



224 



CIVIL ENGINEERING. 



above, the profile is easily transformed. For example, let 
A B C D (Fig. 96) be a cross-section of a wall in which b and 
b' have been determined by previous rule. Let M N be the 
thickness at the middle point of the inner vertical face It is 
evident that if the thickness at top be diminished by C, and 
that at the base be increased by the equal quantity B P, that 
the weight of the wall will remain the same, with an increase 
of stability. 



STRUCTURES OF THE FOURTH CLASS. 

301. Structures belonging to this class sustain a transverse 
strain. Since stone resists poorly a cross-strain, great caution 
must be used in proportioning the different parts of these 
structures. The rules for determining the strength of beams 
subjected to transverse strains can be applied. 



STRUCTURES OF THE FIFTH CLASS. 

302. Arches are the principal structures belonging to this 
class. They are used to transmit the pressure they directly 
receive to lateral points of support. 

Arches are generally made symmetrical, hence the condi- 
tions of stability deduced for either half are equally applica- 
ble to the other. 

303. Modes of yielding. — Arches may yield either by 
sliding along one of their joints, or by turning around an edge 
of a joint. 




Suppose the arch to be divided into equal halves by its 
plane of symmetry, and let the right portion be removed 



ARCHES. 



225 



(Fig. 97). We may sup|X)se the equilibrium preserved by 
substituting a horizontal force II for the half arch removed. 

If the semi-arch were one single piece, the intensity of this 
force, II, could be easily determined, for the conditions of 
equilibrium would require the moment of the weight of the 
semi-arch around the springing line at A to be just equal to 
the moment of II about the same line. 

The semi-arch not being a single piece, but composed of 
several, may separate at any of the joints, and therefore the 
difficulty of determining the values of H is increased. 

CONDITIONS OF STABILITY TO PREVENT SLIDING AT THE JOINTS. 

804. The resistance to sliding arises from the friction of 
the joints and from their adherence to the mortar. 

Arches laid in hydraulic mortar, or thin arches in common 
mortar, may derive an increase of stability from the adhesion 
of the mortar to the joints, but in our calculations we should 
disregard this increase, and depend for stability upon the 
resistance due to friction alone. 

It is found that friction, when the pressure is constant, is 




independent of the area of the surfaces in contact, and de- 
pends solely upon the nature and condition of the surfaces. 

Let F be the resistance to sliding, produced by friction at 

any joint I K (Fig. 98). The external forces acting on this 

15 






h 



r 



<Jr 5-c^_ 



r 



226 CIVIL ENGINEERING. 

joint are the horizontal force H, and the weight of the mass 
K B C I. Denote by R the resultant of these forces, and con- 
struct it. This resultant pierces the plane of the joint I K at 
some poiut as M, and M N will be the normal component. 
Represent by P this normal component, and by S the com- 
ponent parallel to the joint. We have 

F=/P, . 

in whichyis the coefficient of friction determined by experi- 
ment. 

In order that sliding along this joint shall not take place, 
we must have 

S < F, or S < /. P, whence 
S „ 

s 

But p is equal to the tangent of the angle which the result- 
ant R makes with the normal to the joint. Hence we con- 
clude that when the angle made by the resultant of the pres- 
sures with the normal to the surface of the joint is less than 
the angle of friction of the blocks on each other, that there 
will be no sliding. 



CONDITIONS OF STABILITY TO PREVENT RUPTURE BY ROTATION. 

305. Take any joint, as I K (Fig. 98). The arch may give 
way by opening at the back and turning around the lower 
edge at K, or by opening on the soffit and turning around the 
edge at I. 

Let us suppose the first case, or that the arch opens at the 
back. Denote by x the lever arm of the weight W of the 
mass K B C I, and by y the lever arm of the force II, both x 
and y being taken with respect to the edge K. 

For stability we must have 

EL x y - Wx > 0. 

Suppose the second case, or that the arch opens at K, and 
denote by u and v the lever arms of W and II with respect 
to I. We must have for stability 

W x u — II x v > 0. 

X 

If we find the joint for which "VV — is a maximum and 

J y 



JOINTS OF RUPTURE. 227 



u 

W — is a minimum, then for stability against turning around 

any of the edges of the arch we have the condition that the 
thrust II must be greater than this maximum and less than 

this minimum, or, the maximum value of W— must be less 

' ' y 

u 
than the minimum value of W— , and the value of H must lie 



between the two. 



JOINTS OF RUPTURE. 



306. From observations made on the manner in which large 
arches have settled, and from experiments made in rupturing 
small ones, it appears that the ordinary mode of fracture is 
for the arch to separate into four pieces, presenting live joints 
of rupture. 

The segmental arches in which the rise is less than half the 
span, and the full centre arch, yield by the crown settling and 
the sides spreading out. The vertical joint at the crown 




Fig*- 99. 

opens on the soffit, the reins open on the back, and if there 
be no pier, the joints at the springing line open on the soffit 
(Fig. 99). 

The two lower segments revolve outwardly on the exterior 
edge of the joints, leaving room for the upper segments to 
revolve towards each other on the interior edges of the joints 
at the reins. 

This is almost the only mode of yielding for the common 
cylindrical arch. If the thickness be very great compared 
with the span, the rupture will take place by sliding. As a 
rule, this mode of rupture never does take place for the reason 
that the arch will rupture by rotation around a joint before 
it will yield by sliding. 



228 CIVIL ENGINEERING. 

Pointed arches and segmental arches, which are very light, 
and full-centre arches which are slightly loaded at the crown 
and overloaded at the reins, are liable to rupture, as shown in 
Fig. 100. 

In this case the crown rises, the sides fall in, the joints 




Fig. 100. 

open, and the rupture occurs in a manner exactly the reverse 
of that just described. This mode of rupture is still more 
uncommon than that by sliding, and for all these reasons, the 
condition 

H x y - Wx > 

is in general the one applied to test the stability of the arch. 



^CYLINDRICAL ARCH. 

307. Let it be required to find the conditions of equili- 
brium for a full centre arch. 

The strains in the arch are produced by the weight of the 
arch stones, the load placed upon the arch and the reactions 
at the springing lines. 

The object of this discussion is to show how these external 
forces may be determined and how to arrange the joints and 
fix the dimensions of the voussoirs so as to resist successfully 
the action of these forces. 

The joints are the weak places, since the separation of the 
parts at these points is not resisted by the material of which 
the arch is made. 

As before stated, the arch may yield by sliding along one 
of the joints or by turning around an edge. The first mode 
of yielding may be prevented by giving the plane of the joint 
such a position, that its normal shall make with the resultant 
pressure an angle k:ss than the angle of friction of the ma- 
terial of which the voussoirs are made. 



CYLINDRICAL ARCH. 



229 



This is usually effected by making the coursing joints nor- 
mal to the ring courses and to the soffit of the arch. 

Since there is little danger of the arch rupturing by the 
crown rising and the sides falling in, we make use of the 
formula 

II x y-Wx > 0. 

The additional condition is imposed that the whole area of 
the joint must be subjected to compression. It therefore 
follows that the resultant of the external forces must pierce 
the joint within its middle third. 

Since the form of the arch is known, the direction of the 
coursing joints chosen, and the limits of the resultant deter- 
mined, it will only be necessary to find where the resultant 
pierces each joint and see if the angle it makes with the nor- 
mal is less than the angle of friction, and that the resultant 
pierces the plane of the joint within the required limits. 

CYLINDRICAL ARCH UNLOADED. 



308. For simplicity, let us consider the arch to be a full 
centre, the extrados and intrados "being parallel and the 
arch not loaded. 




Fig. 101. 

Let I K (Fig. 101) be a joint of the arch whose thickness 
in the direction of the length of the arch is unity. 
Represent by 

R, the radius of the extrados ; 
r, the radius of the intrados ; 

<£. the angle made by the joint I K with the vertical ; 
W and H, same as in previous case ; 
g, the centre of gravity of the ring KBC I; 
w, the weight of a unit of volume of masonry. 



230 * CIVIL ENGINEERING:. 

The most unfavourable case will be that, when, at or just 
immediately before the time of rupture, the point of appli- 
cation of the horizontal thrust is at C, the highest point of 
the extrados ; the condition of equilibrium is 

W- = H. 

y 

If we find the values of x and y in known terms, and sub- 
stitute them in the expression for the horizontal thrust, the 
latter will be known. 

To find these values of x and y, denote by u the distance 
of the centre of gravity g from 0, and by u L and u 2 the dis- 
tances of the centres of gravity of the sectors I C and K B 
from the same point. We have 

u± x sector I C = u 2 x sector K B + u x ring K BC i. 

The areas of the sectors are -JR 2 </> and ir 2 <f>, hence the area 
of K B C I is equal to £<£ (E 2 -^). 

We find (Anal. Mech., par. 121, p. 96) the values of u x and 

-, 4 o sin i<£ i4 sin i<f> 

u 2 to be - E ±-l and - r £T. 

3 arc 3 arc <t> 

Substituting for the areas, and for u x and u 2 their values 
as above, and solving with respect to u, we have 

3K 2 -^' arc $ * 
Now x is equal to K M — Ug' — r sin cjf> — Og sin i<f>, whence 



x = r sin <f> — — 



4E 3 -r 3 sin 2 1< 



3 E 2 - r arc 

. , 2 E 3 - r s 1 - cos 

= r sin cp — - 

* 3 E 2 - r 2 arc tf> 

and y = E — t 1 cos <£. 

Hence, by writing & for , we have 
H = W- = ?' 2 w * sin (P-l) arc 0- 1(^-1) (1-cos 0), 

y k— COS ^ 

. . (140) 

an expression for the horizontal thrust, in terms of E, r, w, 
and <£, which force applied to the arch at C will prevent the 
rotation of the volume K C B I around the edge K. 



',4<r' 






CYLINDRICAL ARCH. 



231 



This expression might be differentiated with respect to $, 
and that value for <t> obtained, which would make II a maxi- 
mum. This maximum value thus found, if applied to the 
arch at C, would prevent its rotation around any edge on the 
soffit. 

309. Instead of differentiating as suggested, it is usual in 
practice to take the above expression for H, calculate the 
values for every ten degrees, and select fur use the greatest 
of these values. This greatest value thus obtained will differ 
but slightly from the true maximum. 

If we assume h = 1.2, r — 10 feet, R = 12 feet, and w — 
150 pounds, and find the values of H for the different values 
of for every ten degress from 10° to 90°. We may tabu- 
late them as follows : 



Values of <£. 


Values of H in pounds. 


10° 


208 


20° 


670 


30° 


1,127 


40° 


1,450 


50° 


1,625 


60° 


1,675 


70° 


1,662 


80° 


1,490 


90° 


1,285 



A calculation for <f> = 57° gives H = 1,672, 63° gives 1,670, 
and 65° gives 1,661 pounds. 

The angle g£ maximum thrust is very nearly 60°. 

310. The foregoing applies only to an unloaded full centre 
arch, its extrados and intrados being parallel. All arches 
carry loads which frequently rise above the arch to a surface 
either horizontal or nearly so. It is evident that if verticals 
be erected at the joints, and be produced until they meet the 
upper surface of the load, that they will define and limit 
the load resting on each voussoir. An analogous process to 
that just given will enable the student to determine the hori- 
zontal thrust in the arch thus loaded. 



232 CIVIL ENGINEERING. 

Prof. Rankine gives tlie following rule to find the approxi- 
mate horizontal thrust in an arch loaded as shown in the 
figure. (Fig. 102.) . ' 






Fig. 102. 

The horizontal thrust is nearly equal to the weight sup- 
ported between the crown and that jpart of the soffit whose 
inclination is 45°. 

The approximate thrust obtained by this rule seldom differs 
from the true horizontal thrust by so much as one-twentieth 
part. 

Represent by (Fig. 102). 

R, the radius D of the extrados ; 

r, the radius C of the intrados ; 

c, the distance D E, F E being horizontal ; 

w, the weight of a cubic foot of masonry ; 

w', the weight of a cubic foot of the load resting on the 
arch ; 

H. the horizontal thrust required. 

Draw K making an angle of 45° with the vertical ; then, 
the horizontal thrust of the arch on the pier at A is stated to 
be nearly equal to the weight of the mass C K I F E, which 
lies between the joint I K and the vertical plane through C ; 
hence, 

H = W K (.0644 R + .7071 6) + .3927 w (K 2 -*•*). (147) 

for the value of the horizontal thrust. 

The edge I is at the level to which it is advisable to build 
the backing solid, or at least to give the blocks a bond which 
will render the mass effective in transmitting the horizontal 
thrust. 



CURVE OF TKESStJEE. 233 

111 the case of a segmental arch, Rank hie takes the weight 
of half the arch with its load, and multiplies it by the co- 
tangent of the inclination of the intrados, at the springing 
line, to the horizon ; the result is the approximate value of II. 

311. Having determined the value for H for the given 
arch, combine it with the external forces acting on the first 
voussoir at the crown and construct their resultant. The 
point in which this resultant pierces the joint will be the 
centre of pressure for that joint. Do the same for the other 
joints and the intensity of the resultant and the centre of 
pressure for each joint are known. 

The line which is the locus of the centres of pressure for 
each joint is the polygon or line of resistance. Having this 
line determined, the centre of pressure for any joint or section 
is known, but not the direction of the resultant. If a curve 
be drawn tangent to the resultants, this line is called the 
"curve of pressure." 

It is evident, in order to have the conditions of stability 
fulfilled, that, 

The line of resistance must pierce the joint within fixed 
limits ^ and 

The line of pressure must be so situated that a tangent 
drawn to this line, through the centre of pressure of the 
joint, must make an angle with the normal to the joint, less 
than the angle of friction. 

312. Equation of the curve of pressure. — The loads 
placed on an arch are usually symmetrically disposed with 
respect to a vertical plane parallel to the head of the arch. 
The resultant will lie in this plane. 

Take the origin of co-ordinates at (Fig. 103), in which 
A B represents the curve of pressure of an arch loaded as 
stated. Equations (68S) of Anal. Mechanics becoihe for this 
case, 

" >v H-C * = 0, 1 



in which H is the horizontal thrust at ; W, the algebraic 
sum of the vertical forces acting on the arch ; C, the strain 
of compression on any section, as at D ; and s, the length of 
any portion of the curve, as D. 



234 



CIVIL ENGINEERING. 






ruy 



The first of equations (148) shows that the horizontal com- 
ponent of the force of compression at any joint is equal to 
the horizontal thrust at the crown, or is the same at every 
section of the arch. 

The second of these equations shows that the vertical com- 
ponent of the force acting at any joint is equal to the load 
between the vertical plane through the crown and the section 
considered. 

313. Suppose an arch loaded as 
shown in figure (104) ; the material 
being homogeneous and the weight 
of a unit of volume being represented 
by w. Represent F by a. 
Fig. 104. ^he weight of the volume resting 

on the arch between the vertical section at D and the consecu- 
tive section is 

(adx*-\- ydx)w. 

Taking this between the limits, and x, we get 







lax + I ydx \ 



u\ 



for the load resting onO D. Substituting this in the second 
of equations (148) for W, we get 

w (ax xf ydx\ - C ^ = 0. . (149) 

Combining this equation with the first of equations (148), we 
have 

whence, by differentiating, we get 

&-5<- + * •/ ^ 

Integrating this differential equation twice, we get the 
equation of the curve, and find it to be a transcendental line. 

314. If the load had been placed on the arch so as to be a 
dkaet function of. the abscissa, that is, the load between the 
origin and any section whose abscissa was a;, was wx, 
equations (148) would have taken the form 

dx 



then 



1I-C 



</s 



wx — C -j '- 

ds 



0. 



(151) 



CURVE OF PRESSURE. 



235 



Whence, by combination, 



dy = H x ^ x ' 



and by integration, 



y 



w 
2fl 



C = 0. 



(152) 



This is the equation of a parabola. 

315. Polar equation of the curve of pressure. — Gene- 
ral Woodbury deduces the equation of the curve as follows : 

Represent by (Fig. 105) 

H, the horizontal thrust at m ; m up, 
the curve of pressure ; r\ the dis- 
tance, Om,, from pole to the point of 
application, m, of the horizontal 
thrust ; b, the horizontal distance 
between the centre of gravity of the 
segment E F I K C and the vertical 
through C ; A, the area of this seg- 
ment; v, the variable angle nOm, 
and r, the variable distance On. 

For equilibrium, we have 

H (r' — r cos v) = A (r sin v — 5), 
w being considered equal to unity. 

.Whence 




Fig. 105. 



IT/ + Kb 



r = 



A sin v + H cos v 



(153) 



Assuming any joint, the corresponding values of A and b 
for this joint are easily calculated. These being substituted, 
and H and v being known, the corresponding value of r is 
deduced. The curve may then be constructed by points. 

316. A simple inspection of the curve of pressure will 
show where the weak points of the arch are, where the 
heaviest strains are exerted, and where the joints tend to 
open, whether on the soffit or on the back. 

The intrados ought to be parallel to this curve, but in most 
cases the intrados is assumed first and the conditions of equi- 
librium are established afterwards. 

It will be observed that a very heavy load on the arch more 
nearly agrees with the condition of the load being a simple 
direct function of the abscissa, and hence the curve of press- 



A' 



236 CIVIL ENGINEEEFNG. 

ure for this case approaches in form to that of a parabola. If 
we suppose no load on the arch, and neglect the weight of 
the voussoirs, the curve of equilibrium is that of a reversed 
catenary. 

Economy of material would indicate that the intrados and 
extrados should be similar curves. 

317. Depth of keystone. — The form of the arch being 
assumed, the next step is to fix its thickness or depth. The 
power of the arch to resist the horizontal thrust at the crown 
will depend upon the strength of the material of which it is 
made and upon the vertical thickness (depth) of the key. 

The pressure at the extrados of the key, which in general 
is the most exposed part of the joint, should not exceed ^ 
the ultimate strength of the material. Admitting that the 
centre of pressure on this joint may be at one-third of the 
length of the joint from the extrados, we see that in order 
to keep within this limit of y 1 ^, the mean pressure should not 
exceed -fa. 

The celebrated Perronnet gave a rule for determining the 
thickness or depth of the key, which is very nearly expressed 
by the following formula : 

d = -jjr + 0.33 (154) 

d, the depth in metres ; and 

r, the radius of the semicircle, or intrados, in same unit. 
Gen. Woodbury expressed this rule as follows: 
d = 13 inches + -^g-the span. 

For arches with radius exceeding 15 metres, this rule gives 
too great a thickness. 
Prof. Pankine gives 

d= V.~12^" 

in which r is the radius of curvature at the crown in feet. 
His rule is, "For the depth of the keystone, take a mean pro- 
portional between the radius of curvature of the intrados at 
the crown and a constant whose value for a single arch is .12 
feet." 

He recommends, however, in actual practice, to take a 
depth founded on dimensions of good examples already built. 

318. Thickness of piers and abutments. — The stability 
of these may be considered by regarding them either as con- 
tinuations of the arch itself clear to the foundation, or as walls 
whose moment about the axis of rotation is greater than the 
moment of the thrust of the arch. 



THICKNESS OF ABUTMENTS. 



237 



In either case, the student will be able, by applying the 
principles already discussed, to determine the dimensions 
necessary to give the pier, in order that its moment around 
any edge shall exceed the moment of the thrust around the 
same axis. 

The factor of safety is taken at about 2. In piers of great 
height this factor should be increased, while for small heights 
it may be reduced. 

319. Thickness of abutment and depth of keystone 
for small arches. 

The following empirical table is deduced from actual ex- 
amples, and may be used for small arches if made of first- 
class masonry : 

TABLE. 



Span in 


Thickness of Abutment — for heights 


of 


Depth of key- 


feet. 


10 feet. 


15 feet. 


20 feet. 


25 feet. 


stone in inches. 


10 


5 


6 


7 


8 


14 


20 


6 


7 


8 


9 • 


19 


25 


6| 


n 


84 


9£ 


20 


30 


7 


8 


9 


10 


21 


35 


74 


84 


94 


104 


22 


40 


8 


9 


10 


11 


23 


45 


8* 


9* 


104 


m 


24 


50 


9 


10 


11 


12 


25 



If the masonry be second-class, or be roughly dressed, the 
depth of the keystone should be increased about one-fourth. 



FORM OF CYLINDRICAL ARCHES. 



320. As stated before, these arches may be full centre, 
segmental, elliptical, or oval. 

Full centre arches offer the advantages of simplicity of 
form, great strength, and small lateral thrust. But where the 



238 



CIVIL ENGINEERING. 



span is considerable, they require a correspondingly great 
rise, which is often objectionable. 

The segmental arch enables us to reduce the rise, but 
throws a great lateral strain on the abutments. 

The oval affords a means of avoiding both the great rise 
and the great lateral strain, and gives a curve of pleasing 
appearance. 

RAMPANT AND INVERTED ARCHES. 

321. The arch in the preceding cases has been supposed to 
have been upright, and either right or oblique. Rampant 
arches are frequently used ; sometimes the axis is even verti- 
cal. A retaining wall with a semi-circular horizontal section 
would be an example. Arches are often constructed with 
their soffits forming the upper side. These are frequently 
used under openings, their object being to distribute the 
weight equally over the substructure or along the founda- 
tions. They are known as inverted arches, or inverts. The 
principles already laid down for the upright arch apply 
equally to them. 

WOODEN ARCHES. 

322. This term, -wooden arch, is quite often applied to a 
beam bent to a curved shape, its ends being confined so that 
the beam cannot resume its original form. In this shape the 
beam possesses under a load greater stiffness than when it is 
straight. 

A single beam may be used for narrow spans, but built 
beams, either solid or open, must be used for wide ones. 




Fig. 106. 



The load they support rests upon the top of the beams, as 
shown in Fig. 106, or is suspended from them, as shown in 



Fig. 107. 



RUBBLE WALLS. 



239 



Although called arches, they are so only in form, as they 
are not composed of separate pieces held in place by mutual 
pressure. They are now more generally called by their 
proper name, curved beams. 

If we assume that the beam resists by compression alone, 
the dimensions of the beam can be easily determined, in terms 
of the load, of the rise, and the span. 




Fig. 107. 



GRAPHICAL METHOD OF INVESTIGATION. 

323. The graphical method by means of the curve of equi- 
librium is a method much used at the present time for obtain- 
ing the strains on the different parts of the arch. 

This method of investigation will be alluded to in a future 
article. 



CHAPTER X. 

CONSTRUCTION OF MASONRY. 

WALLS OF STONE. 

Stone-masons class the methols of building walls of stone 
into rubble work and ashlar -work. 

I. RUBBLE WORK. 

324. The stones used are of different sizes and shapes, pre- 
pared by knocking off all sharp, weak angles of the blocks 
with a hammer. They are laid in the wall either dry or in 
mortar. If laid without reference to their heights, it is known 
as uneoursed rubble, or common rubble masonry. 



24:0 CIVIL ENGINEERING. 

In building a -wall of rubble (Fig. 108) the mason must 
be careful to place the stones so that they may fit one upon 
the other, filling the interstices between the larger ones by 
smaller ones. Care should be taken to have the vertical 
courses to break joints. 

If laid in mortar, the bed is prepared by spreading mortar 
over the top of the lower course, into which the stone is firmly 
imbedded. The interstices are filled with smaller stones, or 




Fig. 108. 

8tone drippings, and mortar, and finally the whole course 
grouted. 

The mean thickness of a rubble Avail should not be less 
than one-sixth of the height ; in the case of a dry stone wall, 
the thickness should never be less than two feet. It strengthens 
the wall very much to use frequently in every course, stones 
which pass entirely through the wall from the front to the 
back. These are called throughs. If they extend only part 
of this distance, they are called binders. 

325. Coursed rubble, or hammered masonry. — When the 
stones are laid in horizontal courses, and each course levelled 
throughout before another is built upon it, the work is termed 
coursed rubble. As this requires the stones to be roughly 
dressed, or hammered into regular forms before they are laid, 
the work is frequently called hammered, or dressed rubble. 
The same care should be taken in building masonry of this 
kind as that required in the preceding. The mason must be 
particular in making the upper and lower surfaces of each 
stone parallel, and when laying the stones to keep a uniform 
height in each course. If a stone in the course is not high 
enough, other stones are laid on it till the required height is 
obtained. 

The different courses are not each of the same height, but 
vary according to the size of the stone used. The only condi- 
tion required is that each course shall be kept of the same 
height throughout 



ASHLAR MASONRY. 



241 



At the corners, stones of large size, and more acurately 
dressed, are used. These are known as quoins, and are laid 
with care, serving as gauges bv which the height of the course 
is regulated. 



II. ASHLAR WORK. 

326. The stones in tin's kind of masonry are prepared by 
having their beds and joints accurately squared and dressed. 
They are made of various sizes depending on the kind of 
wall to be built and the size of the blocks produced by the 
quarry/ Ordinarily they are about one foot thick, two or 
three "feet long, and have a width from once to twice the 
thickness. They are used generally for the facing of a 
wall, to give the front a regular and uniform appearance, and 
where, by the regularity of the masses, a certain architectural 
effect is to be produced. 

Ashlar work receives different names, from the appearance 
of the face of the "ashlar," and from the kind of tool used in 
dressing it. If the block be smooth on its face, it is called 
plane ashlar (Fig. 109) ; if fluted vertically, tooled ashlar ; 



Fig. 109 — Represents a wall with facing of plane ashlar. 



if roughly trimmed, leaving portions to project beyond the 
edges, rustic ashlar, etc., etc. Rustic ashlar is known as 
rustic, rustic chamfered, rustic work frosted, rustic work 
vermiculated, etc. 

Ashlars are laid in fine mortar or cement. Each one should 
be first fitted in its place dry, so that any inaccuracy in the 
dressing may be discovered and corrected before the stone is 
finally set in mortar. 

To provide for a uniform bearing the stone should be ac- 
curately squared. Frequently the bed is made to slant down- 
16 



242 



CIVIL ENGINEERING. 



wards, from front to back, for the purpose of making close 
horizontal joints in front. This weakens the stone, as the 
weight is thrown forward on the edges of the stones, which 
chip and split off as the work settles. 

327. Walls built with ashlar facing are backed with brick 
or rubble. Economy will decide which is to be used. In the 
construction, throughs of ashlars should be used to bind the 
backing to the facing. Their number will be proportioned to 
the length of the course. The vertical courses break joints, 
each vertical joint being as nearly as possible over the middle 
of the stone below. 




Fig. 110 — Represents a section of wall with faciag of ashlar and a back- 
ing of rubble. 

When the backing is rubble, the method of slanting the bed 
may be allowed for the purpose of forming a better bond 
between the rubble and ashlar ; but, even in this case, the 
block should be dressed true on each joint, to at least one foot 
back from the face. If there exists any cause which would 
give a tendency to an outward thrust from the back, then, 
instead of slanting off all the blocks towards the tail, it will be 
preferable to leave the tails of some thicker than the parts 
which are dressed. 

CUT-STONE MASONRY. 



328. Where great strength is required in the wall, each 
stone is prepared by cutting it to a particular shape, so that 
it can be exactly fitted in the wall ; masonry of this kind is 
called cut-stone. h\ other words, every stone is an ashlar; 



STRENGTH OF MASONRY. 243 

hence the terms cut-stone and ashlar masonry are often 
used one for the other. 

Cut-stone masonry, when carefully constructed, is more 
solid and stronger than any other class. The labor required 
in preparing the blocks makes it the most expensive. It is, 
therefore, restricted in its use to those structures where 
great strength is indispensable. 



STONE-CTJTTING. 

329. The usual method of dressing a surface is to cut 
draughts around and across the stone with a chisel, and then 
work down the intermediate portions between the draughts by 
the use of proper tools. The latter are usually the chisel, axe, 
and hammer. 

No particular difficulty occurs in working a block of stone, 
the faces, beds, and joints of which are to be plane or even 
cylindrical surfaces ; the only difference in method for the 
two being that a curved rule is used in one direction and a 
straight one in another for the cylindrical surface, while for 
the plane surface only one rule is used. 

If the surfaces are to be conical, spherical, or warped, the 
operation is more difficult. It becomes necessary to bring the 
block to a series of plane or cylindrical surfaces, and then 
reduce them to the required form. To show how this can be 
done with the least waste of material is one of the objects of f< jU 



li stereotomy." 



STRENGTH OF MASONRY. fui 

A A 



Strength. — : The strength of masonry will depend on the 
size of the blocks, on the accuracy of the dressing, and on 
the hond. 

330. Size of, stone. — The size of the blocks varies with the 
kind of stone and the nature of the quarry. 

Some stones are of a strength so great as to admit of their 
being used in blocks of any size, while others can only be used 
with safety when the length, breadth, and thickness of the 
block bear certain relations to each other. 

The rule usually followed by builders, with ordinary stone, 
is to make the breadth at least equal to the thickness, and 
seldom greater than twice this dimension, and to limit the 
length to within three times the thickness. When the breadth 
or the length is considerable in comparison with the thick- 



244 CIVIL ENGINEERING. 

ness, there is danger that the block may break, if any unequal 
settling or unequal pressure should take place. As to the ab- 
solute dimensions, the thickness is generally not less than one 
foot, nor greater than two ; stones of this thickness, with the 
relative dimensions just laid down, will weigh from 1,000 to 
8,000 pounds, allowing, on an average, 160 pounds to the 
cubic foot. With these dimensions, therefore, the weight of 
each block will require a very considerable power, both of 
machinery and men, to set it on its bed. 

From some quarries the formation of the stone will allow 
only blocks of medium or small size to be furnished, while 
from others stone of almost' any dimensions can be obtained. 

331. Accuracy of dressing. — The closeness with which 
the blocks fit is solely dependent on the accuracy with which 
the surfaces in contact are wrought or dressed ; if this part of 
the work is done in a slovenly manner, the mass will not only 
open at the joints with an inequality in the settling, but, from 
the courses not fitting acurately on their beds, the blocks will 
be liable to crack from the unequal pressure on the different 
points of the block. 

To comply with the first of the general principles to be 
observed in the construction of masonry, we should have, in a 
wall supporting a vertical pressure, the surfaces of one set of 
joints, the beds, horizontal. This arrangement will prevent 
any tendency of the stones to slip or slide under the action of 
the weight they support. 

The surfaces of the other set should be perpendicular to 
the beds, and at the same time perpendicular to the face, or to 
the back of the wall, according to the position of the stones in 
the mass ; two essential points will thus be attained ; the angles 
of the blocks at the top and bottom of the course, and at the 
face or back, will be right angles, and the block will therefore 
be as strong as the nature of the stone will admit. 

The greater the accuracy of the dressing, the more readily 
can these surfaces be made to fulfil these conditions. 

When a block of cut stone is to be laid, the first point to be 
attended to is to examine the dressing, by placing the block 
on its bed, and seeing that the face is in its proper plane, and 
that the joints are satisfactory. If it be found that the fit is 
not accurate, the inaccuracies are marked, and the requisite 
changes made. 

332. Bond. — Among the various methods used, the one 
known as headers and stretchers is the most simple, and 
offers, in most cases, all requisite solidity; in this method the 
vertical joints of the blocks of each course alternate with the 



BOND. 



245 



vertical joints of the courses above and below it, or break 
joints with them, and the blocks of each course are laid alter- 
nately with their greatest and least dimensions to the face of 
the wall ; those which present the longest dimension along the 
face are termed stretchers, the others headers. (Fig. 111.) 




Fig. Ill — Represents an elevation 
A, vertical section B, and horizontal 
section C, of a wall arranged as 
headers and stretchers. 

a, stretchers. 

5, headers. 



By arranging the blocks in this manner the facing and 
backing of each course are well connected ; and, if any une- 
qual settling takes place, the vertical joints cannot open, as 
would be the case were they continuous from the top to the 
bottom of the mass, for each block of one course confines the 
ends of the two blocks on which it rests in the course beneath. 







A 






..., 




!! 


c:r: 


tr= 




1 1 




" 


" 


1 1 








" 












,itf<W** 


IfcrfjHH 


ttfcrtf«M< 


ttmfHHH 


J. 






\ 



V 



\ 



\ 



Fig. 112 — Represents an elevation A, and perspective views C and D, of 
two of the blocks of a wall in which the blocks are fitted with indents, 
and connected with bolts and cramps of metal. 



246 



CIVIL ENGINEERING. 



333. In masonry exposed to violent shocks, the blocks of 
each course require to be not only very firmly united with 
each other, but also with the courses above and below them. 
To effect this various means have been used. Sometimes the 
stones of different courses are connected by tabling, which 
consists in having the beds of one course arranged with pro- 
jections (Fig. 112) which fit in corresponding indentations 
of the next course. Iron cramps in the form of the letter S, 
set with melted lead, so as to confine the two blocks together. 
Holes are, in some cases, drilled through several courses, and 
the blocks of these courses are connected by strong iron bolts 
fitted to the holes. 

Light-houses, in exposed positions, are peculiarly liable to 
violent shocks from the waves. They are ordinarily, when 
thus exposed, built of masonry, are round in cross-section, and 
solid up to the level of the highest tide. The stones are often- 
times dove-tailed and dowelled into each other, as well as 
fastened together by metal bolts and cramps. 

The maimer of dove-tailing the stones is shown in plan in 
Fig. 113, which represents part of a course where this method 
is used. 




Fio. 113. 



The chief use of the dove-tailing is to resist the tendency of 
the stones to jump out immediately after receiving the blow 
of the wave. This method was first used by Smeaton in build- 
ing the Eddystone light-house. The light-house on Minot's 
Ledge, Massachusetts Bay, built under the superintendence 
of General B. S. Alexander, U. S. Corps of Engineers, by 
the Light-House Board, is a good example of the bond and 
metal fastenings used in such structures. (Figs. 114 and 
115.) 



BOND. 



247 




Fig. 114.— Vertical section showing foundation courses, metal fastenings, 
and the first story above the foundation courses. 




FIG. 115.— Plan of twenty-second course, showing the method of dove- 
tailing the stones. 



248 CIVIL ENGINEERING. 



MACHINERY USED IN CONSTRUCTING WALLS OF STONE. 

334. Scaffolding. — In building a wall, after having raised 
it as high as it can be conveniently done from the ground, 
arrangements must be made to raise the workmen higher, so 
that they can continue the work. This is effected by means 
of a temporary structure called scaffolding 1 . 

If the wall is not used to afford a support for the scaffold- 
ing, two rows of poles are planted firmly in the ground, par- 
allel to the wall, and about four and a half feet apart. These 
uprights in each row are from twelve to fourteen feet apart, 
and from thirty to forty and even fifty feet in height, depend- 
ing upon how high the wall is to be built. 

Horizontal pieces are then firmly fastened to the uprights, 
having their upper surfaces nearly on the same level as the 
highest course of masonry laid. Cross pieces or joists are 
laid on these, and upon them a flooring of boards. Upon 
this platform the masons place their tools and materials and 
continue the work. 

As the wall rises other horizontal pieces are used, and the 
joists and boards carried to the new level. Diagonal pieces 
are used between the rows to brace them together, and in 
each row to stiffen the supports. 

The workmen ascend the scaffolding by means of ladders. 
The materials are hoisted by means of machinery placed on 
the scaffolding or detached from it. 

335. Crane. — The movable or travelling crane, which is 
so arranged as to admit of being moved in the direction of 
the scaffolding and across it, is often used on the scaffolding 
for hoisting the stone. 

Shears, which consist of two or more spars or stout pieces 
of timber, fastened together near the top, and furnished with 
blocks and tackles, are sometimes used. 

The kind of machinery to be used in hoisting the stone 
will be determined by the size of the blocks to be lifted, the 
magnitude and character of the work, and the suitability of 
the site. 

In the United States, the machine known as the " boom 
derrick," or simply " derrick," a modified form of crane, is 
'much used in works of magnitude. 

In the example shown in Fig. 110, the mast is held in a 
vertical position by four guys, generally wire ropes, fastened 
to a ring on the iron cap which is fitted to the top of the 



HOISTING MACHINERY. 



240 



mast Below tins ring, and revolving freely on the cap, is 
a wrought-iron frame containing two sheaves or pulleys. 

The " boom," or derrick, has its outer end supported by a 
topping-lift fastened to this wronght-iron frame. The other 
end fits into an iron socket with collar, or is fastened to the 
wooden frame which embraces the mast, and has a motion of 
rotation around it. The wooden frame bears two windlasses 
and a platform on which the men stand while working them. 
Two tackles are used, one suspended from the outer end of 
the boom, the other from the mast-head, the falls of both 
leading over the sheaves and thence to the windlasses. 




Fig. 116. 



The lower blocks of the tackles are fastened to a triangular 
plate from which a hook is suspended. It is seen that by 
hauling upon or slacking the falls alternately, the stone sus- 
pended from the triangular plate can be placed at any point 
within the circle described by the outer end of the boom. 

336. The blocks of stone are attached to the tackle in 
various ways. Some of the most usual methods are as fol- 
lows : 

I. By nippers or tongs, the claws of which enter a pair of 
holes in the sides of the stone. 

II. By two iron pins let into holes, which they closely fit, 



250 



CIVIL ENGINEERING. 



sloping towards each other (Fig. 117). The force applied to 
the chain to lift the block, jams the pins in their holes. 




, .^iv:.;:;!: 1 :/":";.,;!!! :' : l :"- l l v^ , :.^;:■^^ - , :; ! . :i .' -::-.,::' i :ir;,ir:L,;- 

Fig. 117 — Represents a perspective view of the tackling for hoisting 1 a 
block of stone, A, with draughts around the edges of its faces, and the 
intermediate space axed or knotted. 

a, draughts around edge of block. 

6, knotted part between draughts. 

c, iron bolts with eyes let into oblique holes cut in the block. 

d and e, chain and rope tackling. 

III. By a simple contrivance made of three pieces of iron, 
called a lewis (Fig. 118), which has a dove-tail shape, with 
the larger end downwards, fitting in a hole of similar shape. 
The depth of the hole depends upon the weight and the kind 
of stone to be raised. The tapering side-pieces, ?i, n, of the 
lewis are inserted and placed against the sides of the hole ; 
the middle pieoe, o, is then inserted and secured in its place 
by a pin The stone is then safely hoisted, as it is impossible 
for the lewis to draw out of the hole. 





Fig. 118 — Represents the com- Fig. 119 — A line attached to 

mon iron lewis B. the straight piece, Z>, admits 

??, ?i, side pieces of the lewis. of the latter being drawn 

<?, centre piece of lewis, with out, allowing the piece, ti, 

eye fastened to ?i, n by a boit. to be removed. 

P, iron ring for attaching tackling. 

Where it may not be convenient to reach the pin after the 
stone has been placed in position, a lewis of the form shown 
in (Fig. 119) may bo used. 



BOND. 



251 



WALLS OF BRICK. 



337. Bricks have been referred to in a previous chapter 
as artificial stones. It therefore follows that the general 
principles enunciated for the construction of stone masonry 
are the same for brick as far as they are applicable. 

From the uniformity of size of brick, builders describe the 
thickness of a wall by the number of bricks extending across 
it. Thus, a wall formed of one thickness of brick lying on 
their broad side, with their length in the direction of the 
length of the w T all, is said to be ' k half brick thick." If the 
thickness of the wall is equal to the length of one brick, the 
wall is called " one brick thick," etc. 

The bond used depends upon the character of the struc- 
ture. The most usual kinds are known as the English and 
Flemish. 

338. English bond. — This consists in laying entire courses 
of headers and stretchers periodically, as shown in Fig. 
120. 

Sometimes the courses of headers and stretchers occur 
alternately ; sometimes only one course of headers for three 
or four courses of stretchers. The effect of the stretchers is 
to tie the wall together lengthwise, and the headers, cross- 



1 1 1 1 I 1 1 1 I 1 1 I I 1 I 1 i 1 1 I 1 i 1 - 



I I 1 1 



J L 



I I 



I 1 1 



i_i 



i i n 



i i i i i i i i i i i i i i i i i i i i n 



i i i i i 



iiii i r 



i i i i i i i i i i i i i i i i i i i i i i 

J L 1 1111111 



i i i 



Fig. 120. 



wise. The proportionate number of courses of headers to 
those of stretchers depend upon the relative importance of 
the transverse and longitudinal strength in the wall. 

Since the breadth of a brick is exactly equal to half its 
length, it would be impossible, begriming at a vertical end or 
angle, to make this bond with whole bricks alone. This 
difficulty is removed by the use of a half-brick, made by 
cutting longitudinally a brick in two. A whole brick, used 
as a header, is placed at the corner ; next to this is put a 



252 CIVIL ENGINEERING. 

half -brick. This allows the next header to make the neces- 
sary overlap, which can be preserved throughout the course. 
These ha If -bricks are called closers. 

339. Flemish bond. — This consists in laying headers and 
stretchers alternately in each course. 

A wall built with this bond presents a neater appearance 
than one built in English bond, and this bond is, therefore, 
generally preferred for the fronts of buildings. It is not 
considered as strong as the English, owing to there being, 
ordinarily, a less number of headers in it. 

340. Strengthening of bond. — Pieces of hoop-iron or iron 
lath, so thin that they may be inserted in the joints without 
materially increasing their thickness, add to the strength of 
the bond, especially when hydraulic mortar is used. They 
are laid flat in the bed-joints, and should break joints. It is 
well to nick them at intervals and bend the ends at right 
anodes for the length of two inches, inserting the bent ex- 
tremities into the vertical joints. * 

This method was used by Brunei in forming the entrance 
to the Thames tunnel, and is sometimes designated as 
hoop iron bond. 

341. Hollow masonry. — Hollow brick walls are now ex- 
tensively used in buildings. 

The advantages of hollow walls are economy, lightness, 
and, particularly, freedom from dampness. 

The bricks may be made hollow and laid in the usual way, 
but the usual method of forming the walls is to use ordinary 
brick, and so arrange them in the walls as to leave hollow 
spaces where required. 

342. Strength of brick masonry. — The strength of brick 
masonry depends upon the same three conditions already 
given for stone. Hence, all misshapen and unsound bricks 
should be rejected. 

With good bricks and good mortar a masonry of strength 
and durability nearly equal' to stone is easily formed, and at 
less cost. Its strength is largely due to the strong adhesion 
of mortar to brick. The volume of mortar used is about one- 
fifth that of the brick. 

' 343. Laying the bricks — The strength of brick masonry 
is materially affected by the manner in which the bricks are 
laid. They should not only be placed in positi6n, but pressed 
down firmly into their beds. 

As bricks have great avidity for water, it would always be 
well not only to moisten them before laying, but to allow 
them to soak in water several hours before they are used. 



CONCRETE WALLS. 253 

By taking this precaution, the mortar between the joints will 
set more rlrmly. 

To wet the bricks before they were carried on the scaffold 
would, by making them heavier, add materially to the labor 
of carrying. It is suggested to have arrangements on the 
scaffold where they can be dipped into water, and then 
handed to the mason as he requires them. The wetting is of 
great importance when hydraulic mortar or cement is used, 
for if the bricks are not wet when laid, the cement will not 
attach itself to them as it should. 



MACHINERY OF CONSTRUCTION. 

344. Scaffolding. — In ordinary practice the scaffolds are 
carried up with the walls, and are made to rest upon them. 
The essential features are the same as those used for stone 
walls. It would be an improvement if an inner row of up- 
rights were used instead of the Avail to support the frame- 
work, for the cross-pieces, resting as they do on a single brick 
in a green wall, must exert an injurious influence on it. 

Machinery for hoisting the bricks, mortar, etc., are used in 
extensive works. For ordinary buildings they are taken up 
by workmen by means of ladders. 



WALLS OF CONCRETE. 

345. Concrete masonry. — Within recent years much at- 
tention has been paid to the construction of walls entirely 
of concrete. 

Method of construction. — The concrete is moulded into 
blocks, as previously described, and then laid as in stone ma- 
sonry ; or it is moulded in the wall, forming a monolithic 
structure. 

The walls in the latter case are constructed in sections 
about three feet high and ten or fifteen long. For this pur- 
pose a mould is used made of boards forming two sides of a 
box, the interior width of which is equal to the thickness of 
the wall. Its sides are kept in place by vertical posts, which 
are connected together and prevented from spreading apart 
by small iron rods, as shown in Fig. 121. 

The concrete is shovelled into the mould in layers and 
rammed with a pestle. As soon as the mould is filled, the 
iron rods are withdrawn and the mould lifted up. A. second 



254 



CIVIL ENGINEERING. 



section is formed in like manner on the top of the first, and 

the process goes on until the wall reaches the required height. 

If scaffolding be required in their construction, one of the 

ordinary form may be used, or one like that shown in Fig. 121. 







flljjt 



. 
: r: '-- -: ' : '. ■'...■ '■• " 







Tail's bracket scaffolding, in which the platforms are 
sustained by clamping them to the wall as it is built up, 
using the holes left when the iron rods are withdrawn, is an 
example of one of the devices used in the construction of 
concrete walls ; so also Clarke's adjustable frame, in which 
the platform is supported by a frame from above, fastened to 
clamps embracing the wall. Hoisting apparatus suitable for 
the work is also employed. 

Hollow walls. — In case the wall is required to be hollow, 
a piece of board of the thickness of the required space to be 
left open, and slightly wedge shaped to admit of its being 
easily removed, is laid horizontally in the mould, and the 
concrete rammed in well around it. When the concrete is 
filled to the top of the board, it is drawn out, leaving the re 



CROSS-SECTION OF RETAINING WALL. 255 

quired air space. At regular intervals, ordinary bricks are 
laid as ties to connect together the outer and inner walls. 

Flues, pipes, and other openings for heating, ventilating, 
conveying water, gas, smoke, etc., are constructed in a similar 
manner by using movable cores of the proper size and form. 
Strength and advantages of concrete walls. — It is 
claimed that concrete walls are easier of construction, 
cheaper, and stronger than brick walls of the same thickness, 
and that they possess the great advantage in allowing air pas- 
sages and flues to be easily constructed of uniform size and 
smooth interiors. 



RETAINING AJSTD RESERVOIR WALLS. 

346. Especial care should be taken, in the construction of 
these walls, to secure a firm foundation, and all the pre- 
cautions mentioned in previous articles for laying masonry 
should be observed. 

Thorough drainage must be had, and care be taken to keep 
the water from getting in between the wall and the earth. 
If the latter cannot be avoided, suitable openings through 
the masonry should be made to allow the water to escape. 

When the material at the back of the wall is clay, or is 
retentive of water, a dry rubble wall, or a vertical layer of 
coarse gravel or broken stone, at least one foot thick horizon- 
tally, must be placed at the back of the retaining wall, be- 
tween the earth and the masonry, to act as a drain. 

In rilling in the earth behind the wall, the earth should be 
well rammed in layers inclined downward from the wall. 

Especial care should be taken to allow the mortar to harden 
before letting the wall receive the thrust of the earth. 

Whenever it becomes necessary to form the embankment 
before the mortar has had time to set, some expedient should 
be employed to relieve the wall as far as possible from the 
pressure. Instead of bringing the embankment directly 
against the back of the wall, dry stone or fascines may be 
interposed, or a stiff mortar of clay or sand with about ^th m 
bulk of lime may be used in place of the dry stone. 

347. Form of cross-section of retaining walls. — The 
rectangular and the trapezoidal forms are the most common. 
It is usual, in the latter case, to give the face a batter, varying 
between^ and -M, and to build the back, or side in contact 
with tjre earthyrertical, or in steps. From experiments made 
witlrmodels of retaining walls^ it was shown that as the wall 



256 



CIVIL ENGINEERING. 



gave way, the prism of earth pressing against it did not revolve 
around any line, but settled suddenly and then rested until 
another shock. These experiments seem to coniirm the prac- 
tice of building the back in steps. 

In some cases the wall is of uniform thickness with sloping 
or curved faces. (Figs. 122 and 123.) 








* 



Fig. 123. 



It will be seen that, the weight remaining the same, the 
wall with sloped or curved faces has an increase of stability 
over the corresponding equivalent wall of rectangular cross- 
section. 

The advantage of such' forms, therefore, lies in the saving 
of material. 




Fig. 124. 



Walls with curved batter should have their bed-joints per- 
pendicular to the face of the wall, so as to diminish the obli- 
quity of pressure on the base. (Fig- 124.) 



AND PLATE-BANDS. 



257 



348. Counterforts. — The counterforts are placed along 
the back of the wall, 15 to 18 feet apart, from centre to centre; 
their construction is in every way similar to that recommended 
for retaining walls. 

They should be built simultaneously with the wall, and be 
well bonded into it. 

349. Relieving arches. — The name of relieving arches 
is given to a range of arches resting against the back of a re- 
taining wall to relieve it from the pressure or a part of the 
pressure produced by the earth behind. (Fig. 125.) 




V 



t 



These arches have their axes placed at right angles to the 
back of the wall, and may have their fronts enclosed by the 
earth, as shown in the vertical section represented in Fig. 125. 
There may be one or several tiers of them. 

Knowing the natural slope of earth to be retained, and 
assuming the length of the arch, its height can be deduced, 
or assuming the height, its length may be obtained, so that the 
pressure of the earth on the wall shall not exceed a given 
amount. 

The relieving arches are ordinarily placed about 18 or 20 
feet apart, between their centre lines. The thickness of 
the arch and piers will depend upon the weight they have to 
support. 

AREAS, LINTELS, ETC. 



350. These structures sustain either a vertical pressure up- 
wards or downwards, and are exposed to a cross-strain. 

Area. — It happens sometimes that an upward pressure is 
produced on an area by the presence of water ; this pressure 
must be guarded against. The area of the new capitol at 
17 



258 CIVIL ENGINEERING-. 

Albany, 1ST. Y., is several feet thick, and was made by first 
placing large flat stones over the surface, and then adding 
successive layers of broken stone and concrete. 

Lintels. — The resistance to a transverse strain is very slight 
in stone, therefore the. distance to be spanned by the lintel 
must be quite small, seldom exceeding six feet. 

Plate-bands. — For a similar reason to that just given for 
lintels, the span of a plate-band should not exceed ten feet, 
and all pressure from above should be borne by some inter- 
posing device. 



ARCHES. 

351. The form of the arch is assumed beforehand, and tne 
number and thickness of the voussoirs are afterwards deter- 
mined. The full centre, segmental, and elliptical 'arches 
require no further description, as the student has already 
learned the method of constructing these curves. The vari- 
ous ovals used for the intrados will be the only ones described. 



METHODS OF DESCRIBING OVALS. 

352. The span and rise of an arch being given, together 
with the directions of the tangents to the curve at the spring- 
ing lines and crown, an infinite number of curves, composed 
of arcs of circles, can be determined, which shall satisfy the 
conditions of forming a continuous curve, or one in which the 
arcs shall be consecutively tangent to each other, and such 
that those at the springing lines and the crown shall be tan- 
gent to the assumed directions of the tangents to the curve at 
those points. To give a determinate character to the problem, 
there must be imposed, in each particular case, certain other 
conditions upon which the solution will depend. 

When the tangents to the curve at the springing lines and 
crown are respectively perpendicular to the span and rise, the 
curve satisfying the above general conditions will belong to 
the class of oval or basket-handle curves ; when the tangents 
at the springing lines are perpendicular to the span, and those 
at the crown are oblique to the rise, the curves will belong to 
the class of pointed or obtuse curves. 

The pointed curve gives rise to the pointed or Gothic 
arch. 

[f the intrados is to be an oval or basket-handle, and its 



OVALS OF THREE CENTRES. 



259 



rise is to be not less than one-third of the span, the oval of 
three centres will generally give a curve of a form more pleas- 
ing to the eye than will one of a greater number of centres ; 
but if the rise is to he less than a third of the span, a curve 
of five, seven, or a greater odd number of centres will give 
the more satisfactory solution. In the pointed and obtuse 
curves, the number of centres is even, and is usually restricted 
to four. 

353. Three centre curves. — To obtain a determinate 
solution in this case it will be necessary to impose one more 
condition which shall be compatible with the two general 
ones of having the directions of the tangents at the springing 
lines and crown fixed. One of the most simple conditions, 
and one admitting of a great variety of curves, is to assume 
the radius of the curve at the springing lines. In order that 
this condition shall be compatible with the other two, the 
length assumed for this radius must lie between zero and the 
rise of the arch ; for were it zero there would be but one cen- 
tre, and if taken equal to the rise the radius of the curve at 
the crown would be infinite. 




Fig. 128. 






Let AD (Fig. 126) be the half span, and AC the rise. 
Take any distance less than AC, and set it off from D to R, 
along A D ; and from C to P, along A C. Join R and P, which 
distance bisect by a perpendicular. Prolong this perpen- 
dicular until it intersects the indefinite prolongation of CA. 
Through this point of intersection S and the point R draw an 
indefinite straight line. From R, as a centre, with the radius 
R D, describe an arc, which prolong to Q to intersect S R pro- 














.-- 



260 CIVIL ENGINEERING. 

longed. From S, as a centre, with the radius S Q, describe 
an arc, which, from the construction, must pass through the 
point C, and be tangent to the first arc at Q. The centres R 
and S, thus determined, and the curve DDC described from 
them, will satisfy the imposed conditions. 

354. To construct an oval of three centres, with the 
condition that each of the three arcs shall be of 60°. 

Let A B be the span and A E the rise (Fig. 126). With the 
radius A B describe Bba of 90° ; set off on it Bb = 60° ; draw 
the lines ab, bB, and kb ; from C draw a parallel to ab, and 
mark its intersection c with bB ; from c draw a parallel to 
Ab, and mark its intersections N and with A B, and C A pro- 
longed. From N, with the radius N B, describe the arc Be; 
from 0, with the radius Oc, describe the arc Cc. The curve 
BcC will be the half of the one satisfying the given condi- 
tions, and N and O two of the centres. 

355. To construct an oval of three centres imposing the 
condition that the ratio between the radii of the arcs at the 
crown and springing line shall be a minimum. 

Let A D be the half span, A C the rise (Fig. 126). Draw 
D C, and from C set off on it Cd — Ca, equal to the differ- 
ence between the half span and rise. Bisect the distance Dd 
by a perpendicular, which produce until it intersects C A pro- 
longed. From the points of intersection, R and S, with A D 
and C O as centres, with the radii R D and S Q, describe the 
arcs D Q and Q C ; and the curve D Q C will be the half of 
the one required. 

For, denote by R the radius S C of the arc at the crown, 
by r the radius R D at the springing line, by a the half span 
A D, and by b the rise A C. 

There,, results from the right angled triangle S A R, 

STv^AS^-f AR*, 
or 

(R - rf = (R - b) 2 + (a - rf, 

from which is obtained 

R a 2 + b 2 - 2ar „ , 

— — ~~m ft^ — for the ratio. 

r (26 — 2r)r 

Differentiating this expression, and placing its first differen- 

4-) 

tial coefficient equal to zero, li-i = 0, there results, after the 

ar 
terms are reduced, 



AN OVAL OF FIVE CENTRES. 



261 



a? + b 2 -(a-h) Va 2 + b 2 

2(35 



vv 



+ b 2 / vV + ff -(g-fl)\ 
% \ 2 /' 



l)iit Va* + b' 2 = D C, and vV + ^> 2 — (« — b) = Dd, hence the 



given construction. 



When the rise is less than one-third of the span* ovals of 
three centres are not of so pleasing a shape, and one of five 



>r even a greater number of odd centres must be used 



356. To construct an oval of five centres. 

may be constructed as follows (Fig. 127) : 



This oval 




Fig. 127. 



Let A B be the half span, and A C the rise of the arch. 
Erect at B a perpendicular to A B, and lay off B D equal to 
A C. Join B and C, and through D draw D perpendicular 
to B C, and produce it until it intersects C A prolonged. Lay 
off A H to the right of A equal to A C, and on B H as a diame- 
ter describe the semicircle B E H. From A on A layoff 
A F equal to C E, and with as a centre and F as a radius 
describe the arc F N. Lay off from B, on B A, a distance B L 



262 



CIVIL ENGINEERING. 



equal to A E, and with R as a centre and a radius equal to 
R L describe the arc L N. 

The points 0, N, and R are the centres, and 0Q, N M, and 
R B = R M are the radii of the arcs forming the oval. 

In other ways, by assuming conditions for the radii of the 
two consecutive arcs from the springing line, other ovals of 
five or a greater number may be constructed. 

The curve of the intrados of Perronnet's fine bridge at 
Neuilly, over the Seine, is an oval of eleven centres, the 
radius at the springing line being 21 feet, and at the crown 
159 feet, the span being 128 feet, and the rise 32 feet. 

357. Ovals of four centres, or obtuse and pointed 
curves. — Their constructions are analogous to those already 
given for three centres. For example — 

To construct an oval of four centres. — One method is 
as follows : 

Let A B (Fig. 128) be the half span, A C the rise of the 
required curve and C D the direction of the tangent to it at 




J 



Fig. 128. 



the crown. At C draw a perpendicular to C D. Take any 
point R on A B, such that R B shall be less than the perpen- 
dicular Rb from R upon the tangent C D. From C, on the 
perpendicular to C D, set off Cd equal to the assumed dis- 
tance R B ; draw Rd and bisect it by a perpendicular, which 
prolong to intersect the one from C at the point S ; through 



TUDOR ARCH. 



2G3 



S and R draw a line ; from R, with the radius R B, describe 
an arc, which prolong to Q to intersect the line through S and 
R ; from S, with the radius S Q, describe an arc which will 
be tangent to the first at Q and pass through C. The curve 
B Q C will be the half of the one required to satisfy the given 
conditions. 

The four- centred Tudor arch is generally constructed as 
follows : 

Let A B (Fig. 129) be the span, and divide it into four equal 
parts, the points of division being D, C, and D'. 




Fig. 129. 



From D and D', with a radius equal to D D', describe arcs 
intersecting at E. Through E draw the lines D E and D'E, 
and produce them until they intersect the perpendiculars to 
the span through D and D'. With the radius D A describe 
the arc A F, and with the radius O'F the arc F H. The other 
half is drawn in a similar manner. 

358, Voussoirs. — The form of intrados and depth of key- 
stone being determined, the form of the extrados and the 
number of voussoirs are then fixed. The shape and dimen- 
sions of the voussoirs should be determined both by geometri- 
cal drawings and numerical calculation, whenever the arch is 
important, or presents any complication of form. The draw- 
ings should be made to a scale sufficiently large to determine 
the parts with accuracy, and from these, pattern drawings 






264 CIVIL ENGINEERING. 

may be constructed giving the parts in their true size. To 
make the pattern drawings, the side of a vertical wall or a firm 
horizontal area may be prepared with a thin coating of mor- 
tar, to receive a thin, smooth coat of plaster of Paris. The 
drawing is then made on this prepared surface by construct- 
ing the curve by points from its calculated abscissas and ordi- 
nates, or, where it is formed of circular arcs, by using the ordin- 
ary instruments for describing such arcs when the centres 
fall within the limits of the prepared surface. To construct 
the intermediate normals, whenever the centres of the arcs do 
not fall on the surface, an arc with a chord of about one foot 
may be set off each side of tin* point through which the 
normal is to be drawn, and the chord of the whole arc, thus 
set off, be bisected by a perpendicular. This construction 
will generally give a sufficiently accurate practical result for 
elliptical and other curves if of a large size. 

From the pattern drawings thus constructed, templets and 
bevels are made which guide the stone-cutter in shaping the 
angles and surfaces of the voussoirs. 

The methods of representing the voussoirs by projections, 
and from them deducing the true dimensions and forms of 
the joints, are discussed in " Stone Cutting." 

359. Bond. — The same general principles are followed in 
arranging the joints and bond of the masonry of arches, as 
in other masonry structures. The surfaces of the joints 
should be normal to the soffit, and the surfaces of any two 
systems of joints should be normal to each other at their lines 
of intersection. These conditions, with respect to the joints, 
will generally be satisfied by tracing upon the soffit its lines 
of least and greatest curvature and taking the edges of one 
series of joints to correspond with one of these systems of 
lines, and the edges of the other series with the other system, 
the surfaces of the joints being formed by the surfaces nor- 
mal to the soffit along the respective lines in cpiestion. When- 
ever the surface of the soffit is a single curved surface, the 
joints will be thus either plane or developable surfaces. 

Hence, in the right cylindrical arch the edges of one series 
of joints will correspond to the right line elements of the 
cylindrical surface, while those of the other will correspond 
to the curves of right section, the former answering to the 
line of least, and the latter of greatest curvature. The sur- 
faces of the joints will all be plane surfaces, and, being 
normal to the soffit along the lines in cpiestion, will be nor- 
mal also to each other. 

In full centre and segmental arches, the voussoirs are 



OBLIQUE ARCHES. 



265 



visually made of the same breadth, estimated along the curve 
of right section. In the right cylindrical arches of other 
forms of right section, it may not in many cases be. practi- 
cable to give to all the vonssoirs the same breadth, owing to 
the variable curvature of the right section; but the arrange- 
ment is the same throughout all the ring courses. 

360. Oblique or askew arches. — When the obliquity is 
slight, the arch is built of equal separate ribs, each rib slightly 
overlapping the other, or, the obliquity is obviated by using 
piers of trapezoidal horizontal section. If the obliquity be 
considerable, a different method mnst be pursued. 

In order to avoid the pressure being oblique to the cours- 
ing joints, the latter cannot be made parallel to the axis of 
the arch. The difficulties thus originated have caused the 
askew arch to be used very little in this country. 

The best form for the edges of the heading joints would 
be the curves cut out of the soffit by vertical planes, passed 
parallel to the head of the arch. The edges of the coursing 
joints will then be found, by tracing on the soffit, curves at 
right angles to the edges of the heading joints. This method 
is the one principally used in France (Fig. 130). It gives 
unequal width on the soffit to the vonssoirs, and therefore 
makes it inapplicable to brick masonry. The joints are also 
difficult of execution. 




Fig. 130. — Elevation of the head and a portion of the soffit of an oblique 
cylindrical arch, with the edges of the conrsing joints at right angles to 
the edges of heading joints, which latter are parallel to the curves of the 
heads of the arch. 

The letters refer to same parts as in next figure. 



The method most commonly used in England consists in 
placing the edges of the joint along spiral lines (Fig. 131) 



of the soffit, intersecting each other at 



riidit 



angles. The 



$66 



CIVIL ENGINEERING. 



spirals for the edges of the heading joints are drawn parallel 
to the spiral which passes through the ends of the span and 
rise of the head of the arch ; the spirals for the edges of the 




Eia. 131. — Elevation, A, of the head and of a part of the soffit, B, of an 

oblique cylindrical arch with spiral joints. 
a, voussoirs of cut stone, 
c, c, bottom course of stone voussoirs cut to receive the brick courses. 

C, face of the abutment. 

D, ends of the abutments. 

coursing joints being traced on the soffit perpendicular to the 
first set of spirals. 

The above are the two principal methods used for import- 
ant arches of considerable obliquity. 



MATERIALS USED IN CONSTRUCTING ARCHES. 

Arches may be either of stone, brick, or mixed masonry. 

361. Arches of stone. — In wide spans, and particularly in 
flat arches, cut stone alone should be used. 

Rubble stone may be used for very small arches, which do 
not sustain much weight, or as a filling between a network of 
the ring and string courses of larger ones. In both cases the 
blocks should be roughly dressed with the hammer, and the 
best of mortar should be used. 

362. Arches of brick. — Brick may be used alone or in 
combination with cut stone for arches of considerable size. 
The brick used may be wedge-shaped, or of the common 
form. In the former case there is no difficulty in their 
accommodating themselves to the curved slfape of the 
arch. In the latter case this can be effected by making 
the joints 'thicker towards the extrados than towards the 
intvados. 

Brick arches are often built in concentric rings, each half 



ARCHES OF MIXED MASONRY. 267 

a brick thick, the connection of the rings depending upon the 
tenacity of the mortar. Continuous joints are thus formed 
parallel to the soffit, and are liable to yield on the arch 
settling. The layers are called shells. This method should 
not be used in arches of more than thirty feet span. Another 
mode of construction is to lay the bricks in ordinary strjng 
courses. In this method continuous joints are formed, ex- 
tending from the soffit outward ; they are necessarily very 
open at the back, and must be filled with mortar, pieces of 
slate, or other material. 

To obviate the defects of both methods as much as possible, 
the arch may be constructed by building partly in one way 
and partly in the other; or, as it is termed, in shells and 
blocks (Fig. 132). This method is to use blocks of brick- 
work built as solidly as possible, separated at short intervals 
by portions of concentric rings. The bricks in the blocks 




Fig. 132 



should be moulded or rubbed down to the proper form, 
especially in arches of importance. Pieces of hoop-iron laid 
in the joints would increase the strength of the bond. 

363. Arches of mixed masonry. — When a combination 
of brick and cut stone is used, the ring courses of the heads, 
with some intermediate ring courses, the bottom string 
courses, the key-stone course, and a few intermediate string 
courses, are made of cut stone, the intermediate spaces being 
filled with brick (Fig. 133). 

The voussoirs which form the rino; course of the heads are 



268 



CIVIL ENGINEERING. 



usually terminated by plane surfaces at the top and on the 
sides, for the purpose of connecting them with the horizontal 




Fig. 133. 



courses of the head, which lie above and on each side of the 
arch (Figs. 134 and 135). 




Fig. 134. 




Fig. 135. 



This connection may be made in various ways. The points 
to be observed are to form a good bond between the voussoirs 
and horizontal courses, and to give a pleasing architectural 
effect. 

Sometimes the voussoir is so cut as to form an elbow-joint, 
as shown at 0, 0, in Fig. 134. This is objectionable both on 
account of waste of material in the cutting and from the 
liability of the stone to split when the arch settles. 

364. Cappings. — When the heads of the arch form a part 
of the exterior of a structure, as when they are the faces of a 
wall or the outer portions of a bridge, then the top surface 
of the voussoirs of the ring courses, between the heads, is 
usually left in a roughly dressed state to receive the courses 
of masonry, termed the capping, which rest upon the arch 
between the walls of the head. Before laving the capping, 
the joints of the voussoirs on the back of the arch should be 
carefully examined, and, wherever they are found to be open 
from the settling of the arch, they should be filled. 



ABUTMENTS AND PIEKS. 269 

The capping may be of brick, rubble, or concrete. "When 
the arches are exposed to filtration of rain-water, as in bridges, 
casemates of fortifications, etc., the capping should be made 
water-tight. 

The difficulty of forming water-tight cappings of mason ly 
has led engineers to try a covering of asphalt laid upon con- 
crete. This asphalt is put on as previously described, using 
sometimes several coats, care being taken to make the squares 
of each successive layer break joints with the preceding. 

In a range of arches, like those of bridges or casemates, 
the top of the capping of each arch forms two inclined sur- 
faces, like those of a common roof. The bottom of these 
surfaces, by their junction, form gutters where the water col- 
lects, and from which it is conveyed off in conduits, formed 
either of iron pipes or of openings made through the masonry 
of the piers. 

When the spaces between the head walls above the capping 
is filled in with earth, a series of drains should be made run- 
ning from the top or ridge of the capping, and leading into 
the main gutter drain. They are made of dry brick laid flat, 
with intervals, being covered by other courses of dry brick 
with open joints. 

365. Abutments and piers. — The same care and precau- 
tions recommended in constructing retaining walls apply 
equally to the construction of abutments and piers. 

When abutments, as in the case of buildings, require to be 
of considerable height, and would therefore demand extraor- 
dinary thickness if used alone to sustain the thrust of the 
arch, they may be strengthened by carrying them up above 
their connection with the arch, thus adding to their weight, 
as in the battlements and pinnacles of Gothic architec- 
ture ; by adding to them ordinary, full, or arched buttresses, 
termed flying buttresses; or by using ties of iron below 
the key-stone to connect the voussoirs which are near the 
joints of rupture. The employment of these different expe- 
dients, their forms and dimensions, will depend on the char- 
acter of the structure and the kind of arch. The iron tie, 
for example, cannot be hidden from view except in the plate- 
band, or in very fiat segmental arches, and wherever its ap- 
pearance would be unsightly some other expedient must be 
tried. 

366. Connection of the arch with its abutment. — 
Care should be taken to make a firm connection between the 
lowest courses of the arch and the top of the abutment, par- 
ticularly in the askew and segmental arches. 



270 CIVIL ENGINEERING. 

The top stone of the abutment, or cushion stone, should be 
well bonded with the stones of the backing ; should be made 
thick enough to resist the pressure brought to bear on it ; and 
made secure against any sliding. 



MACHINERY USED IN CONSTRUCTION. 

367. Scaffolding and hoisting arrangements are necessary, 
and are in all things similar to those used for other stone 
masonry. In addition, a construction called centerings are 
used. From the nature of an arch, formed as it is of separate 
pieces, it is evident that it could not be placed in position 
without some artificial support for the blocks to rest upon 
during construction. When the arch is completed the arti- 
ficial support is removed, leaving clear the space arched over. 
This artificial support is called the centre or centering of 
the arch, and is made generally of wood. 

A centre may be defined to be a wooden frame which 
supports the vonssoirs while the arch is in progress of con- 
struction. 

It consists of a number of vertical frames, termed ribs, 
upon which horizontal beams, called bolsters, are placed to 
receive the voussoirs of the arch. These ribs are placed 
from five to six feet apart, and have the upper or bearing 
surface curved to a figure parallel to that of the soffit of the 
,arch. For an arch of considerable weight, the pieces form- 
ing the back of the centre on which the bolsters rest consist 
of beams of suitable lengths shaped to the proper ♦curvature 
and abutting end to end, the joints between them being nor- 
mal to the curved surface. The joints are usually secured by 
short pieces, or blocks, placed under the abutting ends aud to 
which the pieces are bolted. The blocks are shaped so as to 
form abutting surfaces for struts which rest against them and 
against firm points of support beneath. To prevent the struts 
from bending, braces or bridle pieces are used, and the 
whole frame is firmly connected by iron bolts. 

This describes the general construction of a centre. The 
position of the points of support and the size of the arches 
will affect materially the combinations of the parts. 

If for a light arch, as that thrown over a window or a 
door, planks instead of beams are used to form the bark, and 
two ribs onlv arc required. Their construction is shown in 
(Fig. I ::<■>). " 



CONSTRUCTION OF CENTRES. 



271 



In the figure, the centre is shown resting on the walls. If 
the intrados is to be tangent to the inner face of the walls, 




Fig. 136. 



supports must be placed next to the wall, as shown in Fig. 
137, to hold up the centre. 




If the arch be heavier, an arrangement such as shown in 
Fig. 137 may be used, in which the back may consist of two 
or three thicknesses of plank nailed together, or of pieces of 
scantling of proper size. 

The points to be considered in the construction of centres 
are, that the upper or bearing surface shall be correctly 
formed ; that the centre shall be strong enough to bear the 



272 



CIVIL EKGINEEEING. 



load which is to be placed upon it, that is to support the 
weight of vonssoirs, workmen, tools, etc., without sinking or 
changing its form during the construction of the arch; and 
that it may be easily and conveniently removed without in- 
jury when the arch is completed. 

The most important centerings are those used in the con- 
struction of bridges of wide span, and for domes of impor- 
tant public buildings. 

368. General remarks. — The rules given for laying ash- 
lar or cut-stone masonry should especially be strictly observed 
in the construction of arches. The manner of laying the 
voussoirs which form the head of the arch demands peculiar 
care. The building of the arch should be carried up simul- 
taneously at the two sides of the centering, so that its con- 
struction should not be more rapid on one side than on the 
other. The loading on the centre will in this way be kept 
symmetrical. 

The centres, particularly of large arches, should not be re- 
moved until the mortar has set; it is recommended that, after 
removing the centre, the arch should be allowed to settle and 
assume its permanent state before any load is placed upon it. 




Fig. 138. 



Very flat arches and plate-bands over doorways or wide 
openings in a wall have segmeotal arches placed above (Fig. 
138) to relieve; them from the weight oi the wall which 



GENERAL PRINCIPLES. 273 

otherwise would rest upon them. From the object of these 
additional arches, they receive the name of relieving 
arches. 

The principles of the arch should be thoroughly under- 
stood by the engineer as well as the architect. 

The form of the arch will depend upon the purposes which 
it has to serve, the locality, and the style of architecture. 

The full centre arch is the strongest, and should be used 
when great strength is required and no limit to the rise is 
imposed. The elliptical is regarded the most graceful arch, 
the segmental as the most useful. 

Pointed arches are used in buildings, especially those of the 
Gothic order, but are not as a rule used for bridges or similar 
structuress 

369. Origin and use of the arch. — It is a matter in ques- 
tion as to what country or people the world is indebted for the 
arch. But there is no doubt that Europe is indebted to the 
Romans for the general use of the arch in building. The full 
centre and segmental arches especially were much used by 
them in the construction of both public *and private works, as 
temples, palaces, private residences, baths, sewers, bridges, 
aqueducts, etc., whose remains are still to be seen. They were 
the first to use the dome for covering their temples. 

Afterwards, the arch under various forms became an essen- 
tial element in the construction of buildings throughout Eu- 
rope. And still later it forms in the United States a promi- 
nent feature of all our constructions, although it has not by 
us been used to the same extent in bridges as by Europeans. 



GENERAL PRINCIPLES TO BE OBSERVED IN THE CONSTRUCTION OF 

MASONRY. 

370. From what has preceded, the following general prin- 
ciples may be stated : 

1. To build the masonry in a series of courses, which shall 
be perpendicular, or' as nearly so as practicable, to the direc- 
tion of the force which they have to resist. 

2. To avoid the use of continuous joints parallel to the 
direction of the force. 

3. To use the largest stones in the lower courses. 

4. To lay the lower courses, the force acting vertically, on 
their natural bed. "Where great strength is required in these 
courses, the beds should be dressed square. 

5. To moisten all dry and porous stones before bedding 

18 



274 CIVIL ENGINEERING. 

them in mortar, and thoroughly cleanse from dust, etc., their 
lower surfaces, and the bed of the course on which they are 
to be laid. 

6. To reduce the space between each stone as much as pos- 
sible, and to completely fill the joint with mortar. 



PRESERVATION OF MASONRY. 

371. When the joints of masonry are laid in common mor- 
tar, it is usual to protect the surface exposed to the weather 
by pointing them. 

In pointing, the joint is cot out to the depth of about an 
inch, brushed clean, and moistened with water ; the pointing 
mortar is then applied with a suitable tool for pressing it into 
the joint and its surface rubbed smooth with an iron tool. The 
practice with the United States engineers is to calk the joints 
with a hammer and calking-iron and to rub the surface of the 
pointing with a steel polishing tool. 

The pointing mortar is made of a paste of finely -ground 
cement and clean, sharp sand, about one measure of cement 
paste to two and a half of sand ; or, if mixed dry, one of 
cement to three of sand by weight. It is made in small 
quantities at a time, the ingredients being mixed are placed 
in an iron mortar with a little water, and thoroughly incor- 
porated by pounding with an iron pestle. 

The period at which pointing should be done is not fully 
agreed upon by builders, some preferring to point while the 
mortar in the joint is still fresh, or green, and others not 
until it has become hard. The latter is the better plan ; the 
former is the cheaper, as the joints are more easily cleaned out. 

To obtain pointing that will withstand the changes of our 
climate is not the least of the difficulties of the builder's art. 
The contraction and expansion of the stone causes the point- 
ing to crack, or to separate from the stone, and the water 
penetrating into the cracks thus made, throws out the point- 
ing when acted upon by frost. Some have tried to meet this 
difficulty by giving the surface of the pointing such a shape, 
and so arranging it with respect to the surfaces of the stones 
forming the joint, that the water shall trickle over the point- 
ing without entering the crack usually found between the bed 
of the stone and the pointing. 

37'2. Flash-pointing is a term sometimes applied to a thin 
coating of hydraulic mortar, made with a largo proportion of 
hydraulic cement, laid over the face or back of a wall to pro- 



PRESERVATION OF MASONRY. 275 

tect the joints or the stone itself from the action of moisture 
and the weather. 

When used to protect the stone, the sand in the mortar 
should be coarse, and the mortar applied in a single uniform 
coat over the surface, which should be thoroughly cleansed 
from dust and loose mortar, and well moistened before the 
applicatioD is made* 

373. Precautions against unequal settling. — A certain 
amount of settling always takes place *in masonry, due to the 
shrinkage of the mortar and other causes, and the engineer 
must take every precaution to ensure that this settling shall 
be equal throughout. Otherwise, especially in parts sustain- 
ing unequal loads, and which are required to be firmly joined 
together, the unequal settling that takes place is accompanied 
by cracks and ruptures in the masonry. 

To avoid this unequal settling, it is advised to use the same 
thickness of mortar throughout, to pay particular attention to 
the bond and correct fitting of the courses, and to carry up 
all parts of the wall simultaneously. If the walls are to be 
subjected to heavy vertical pressures, it is recommended to 
take the further precautions of using hydraulic instead of 
common mortal*, of requiring the materials to be uniform in 
size and quality, and of delaying putting the permanent load 
on the wails until the season after the masonry is laid. It is 
also suggested to use a proof load, when practicable, before 
placing on the permanent one. 

374. Effects of temperature on masonry. — Frost is the 
most powerful destructive agent against which the engineer 
has to guard in masonry constructions. During severe winters 
in the northern parts of our country, it has been ascertained,. 
by observation, that the frost will penetrate earth in contact 
with walls to a depth of ten feet; it therefore becomes a 
matter of the first importance to use every practicable means 
to drain thoroughly all the ground in contact with masonry 
to whatever depth the foundations may be sunk below the sur- 
face ; for if this precaution be not taken, accidents of the 
most serious nature may happen to the foundations from the 
action of the frost. If water is liable to collect in any quan- 
tity in the earth around the foundations, it may be necessary 
to make small covered drains under them to convey it off, and 
to place a stratum of loose stone between the sides of the 
foundations and the surrounding earth to give the water a free 
downward passage. 

It may be laid down as a maxim in building, that mortar 
exposed to the action of frost before setting will be so much 



276 CIVIL ENGINEERING. 

damaged as to impair materially its properties. This fact 
shows the necessity of laying the foundations and the struc- 
ture resting on them in hydraulic mortar to a height of at 
least three feet above the ground ; for although the mortar of 
the foundations might be protected from the action of the 
frost by the earth around them, the parts immediately above 
would be exposed, and as those parts attract the moisture from 
the ground, the mortar; if of common lime, would not set in 
time to prevent the action of the frosts of winter. 

In heavy walls the mortar in the interior will usually be 
secure against the action of the frost, and masonry of this 
character might be carried on until freezing weather com- 
mences ; but in all important works it will be the safer course 
to suspend the construction of masonry several weeks before 
the ordinary period of frost. 

During the heat of summer the mortar is apt to be injured by 
drying too rapidly. To prevent this the stone or brick should 
be thoroughly moistened before being laid ; and afterwards, 
if the weather is very hot, the masonry should be kept wet 
until the mortar gives indications of setting. The top course 
should always be well moistened by the workmen when quitting 
their work for any short period during very warm weather. 

The effects produced by a high or low temperature on mor- 
tar in a green state are similar. In the one case the freezing 
of the water prevents a union between the particles of the 
lime and sand ; and in the other, the same result arises from 
the water being rapidly evaporated. In both cases the mortar 
is weak and pulverulent when it has set. 

375. Repairs of masonry. — In repairing masonry it is 
necessary to connect the new work with the old. To do this, 
the surface of the old, where the junction is to be made, 
should be arranged in steps and the mortar along this surface 
be scraped and cleaned. The new work is then joined to the 
steps by a suitable bond, care being taken to have the surfaces 
fitted accurately, and to use the least amount of mortar that 
will effect the required object. 

MENSURATION OF MASONRY. 

376. Engineers, when measuring or estimating quantities 
of masonry, state them in cubic feet or yards. Builders and 
contractors often use other mode's, as perches of stone, rods of 
brickwork, etc. To avoid misunderstanding, the engineer 
should inform himself of the modes used in the locality where 
his work is to be built. 



PART V. 



CHAPTEE XI. 

FOUNDATIONS. 

377. The term, foundation, is used to designate the lowest 
portion or base of any structure. 

This term is frequently applied to that portion of the solid 
material of the earth upon which the structure rests, and also 
to the artificial arrangements which may be made to support 
the base. 

It is recommended to restrict the use of the term, founda- 
tion, to the lower courses of the structure, and to use the 
term, bed of the foundation, when either of the other two 
are meant. 

37S. In the preceding chapters, the foundations of the 
structures there considered have been regarded as secure. 
Since the permanence of structures depends greatly upon the 
safety of the foundations, it is plain that the importance 
attached by engineers to the proper construction of them 
cannot be over-estimated. 

379. Foundations are liable to yield either by sliding on 
their beds or by turning over by rotation about one of the 
edges. In general, if care is taken to prevent rotation, there 
need be no fear of yielding by sliding, especially if the bed is 
a hard ground or other compact material. 

If the bed is of a homogeneous material and the pressure 
borne by the foundations is uniformly distributed over it, 
there will be no tendency to overturn, and the settling, which 
always exists to a greater or less extent, will be uniform 
throughout. 

If the material forming the natural bed is not homogeneous, 
or the centre of pressure does not coincide with the centre of 
figure of the base, unequal settling will take place, followed 
by cracks and ruptures in the masonry, and finally, under 
certain circumstances, bv the destruction of the work. 



278 CIVIL ENGINEERING. 

The ma*in objects to be attained, in preparing the bed and 
foundation of any structure, are to reduce the settling to the 
smallest possible amount, and to prevent this settling from 
being unequal. 

380. The beds of foundations are divided into two classes : 

1. Natural beds, or those prepared in soils sufficiently 
firm to bear the weight of the structure ; and 

2. Artificial beds, or those which require an artificial ar- 
rangement to be made to support the structure, in consequence 
of the softness or want of homogeneousness of the soil. 

Before a selection of the kind of bed can be made, it is 
necessary to know the nature of the subsoil. If this is not 
already known, it is determined ordinarily by digging a 
trench or sinking a pit close to the site of the proposed work, 
to a depth sufficient to allow the different strata to be seen. 
For important structures, the kind of subsoil is frequently 
made known by boring with the tools usually employed for 
this purpose. 

When this method is used, the different kinds and thick- 
nesses of the strata are determined by examining the speci- 
mens brought up by the auger used in boring. 

381. Soils are divided, with reference to foundations, into 
three classes : 

1. Those composed of materials whose stability is not 
affected by saturation with water, and are firm enough to 
support the weight of the structure. 

2. Those firm enough, but whose stability is affected by the 
presence of water. 

3. Compressible or soft soils. 

Rock, compact stony earths, etc., are examples of the first 
class ; clay, sand, fine gravel, etc., are examples of the sec- 
ond ; and common earth, marshy soils, etc., are examples of 
the third. 

The beds are prepared either on land or under the water. 



FOUNDATIONS ON LAND. 

There will be three cases, corresponding to the three kinds 
of soil in which the bed is to be prepared. 

I. BEDS PREPARED IN SOILS OF THE FIRST CLASS. 

382. Rock. — AVlum rock forms the material in which the 
bed is to be made, it is only necessary to ascertain if the rock 



FOUNDATIONS ON LAND. 279 

has a sufficient area, is free from cavities, and sufficiently thick 
to support the structure without danger of breaking. If the 
rock be found too thin, the nature of the soil on which it 
rests must be determined. If there are any doubts on any 
of these points, a thorough examination into the thickness of 
the stratum and tests upon its strength should be made. It 
is also recommended, in case of important structures, to test 
further its strength by placing on it a trial weight, which 
should be at least twice as great as that of the proposed 
Structure. 

Having become satisfied with the strength of the rock, all 
the loose and decayed portions are removed and the surface 
levelled. If some parts are required to be at a lower level 
than others, the bed should be broken into steps. Fissures 
should be filled with concrete or rubble masonry. If this 
should be too expensive, arches should be thrown over them. 
In some cases, it is advisable to cover the whole surface of 
the rock with a layer of concrete. 

The load placed on the rock should not exceed the limit of 
safety. This limit is taken usually at one-tenth of the load 
necessary to crush the rock. 

A bed in solid rock is unyielding, and appears at first sight 
to offer all the advantages of a secure foundation. It is found 
in practice, that in large buildings some portions will not rest 
on the rock, but on some adjacent material, as clay or gravel. 
Irregularity of settlement will in such cases almost invariably 
follow, and gives great trouble. 

383. Compact stony earths, etc. — The bed is prepared 
in soils of this kind by digging a trench deep enough to 
place the foundation below the reach of the disintegrating 
effects of frost. A depth of from four to six feet will gen- 
erally be sufficient. 

The bottom of the trench is made level, both transversely 
as well as longitudinally, and if parts of it are required to be 
at different levels, it is broken into steps. Care should be 
taken to keep the surface water out of the trench, and, if 
necessary, to have drains made at the bottom to carry away 
the water. 

The weight resting on the bottom of t'he trench should be 
proportioned to the resistance of the material forming the 
bed. The limit for a firm soil of this class is about twenty- 
five pounds per square inch. 

It is usual, iii order to distribute the pressure arising from 
the weight of the structure over a greater surface, to give 
additional breadth to the foundation courses, which increase 



* 

280 CIVIL ENGINEERING. 



of breadth is called the spread. In compact stony earth, the 
spread is made once and a half the thickness of the wall, and 
in ordinary earth or sand twice that thickness. 



II. BEDS IN SOILS OF THE SECOND CLASS. 

384. The bed is prepared in a soil of this kind by digging 
a trench, as in the previous case, deep enough to place the 
foundation of the structure below the injurious effects of 
frost. Since the soil is effected by saturation with water, the 
ground should be well drained before the work is begun, and 
the trenches so arranged that the water shall not remain in 
them. And in general, the less a soil of this kind is exposed 
to the air and weather, and the sooner it is protected from 
exposure, the better for the work. 

In this case, as well as in the preceding, it was supposed 
that the layer of loose and decayed materials resting on the 
soil iii which the bed is to be prepared was of moderate 
depth, and that the thickness of the stratum in which the bed 
is made was sufficient to support the weight of the structure. 

it sometimes happens that this firm soil in which the bed 
is to be made rests upon another which is compressible, or 
which is liable to yield laterally. In such situations, the 
weight of the structure should be reduced to its minimum, 
and should be distributed over a bearing surface sufficiently 
large to keep the pressure on any portion of the bed within 
certain limits. If there is any danger from lateral yielding, 
the bed must be secured by confining the compressible or 
yielding soil so it cannot spread out. This may be done by 
using sheeting piles, or other suitable contrivance. 



III. BEDS IN SOILS OF THE THIRD CLASS. 

385. In soft earths.— The bed is prepared, as in the other 
cases, by digging a trench sufficiently deep to place the foun- 
dation courses below the action of frost and rain. 

Greater caution, however, must be observed in a case of 
this kind than in any of the proceeding, to prevent any un- 
equal settling. 

The bottom of the trench should be made level and covered 
with a bed of stones, sand, or concrete, 

[f stone be used, it is the practice to pave the bottom of 
the trench with nibble or cobble stones, which are well set- 



BEDS IN SOFT EARTHS. 



281 



tied in place by ramming, and on this paving lay a bed of 
concrete. 

If sand is used, the sand is spread in layers of about nine 
inches in thickness, and each layer well rammed before the 
next one is spread. The total depth of sand used should be 
sufficient to admit of the pressure on the upper surface of the 
sand being distributed over the entire bottom of the trench. 
(Fig. 139.) 





Fig. 139. 



Fig. 140. 



Another method of using sand for this purpose is to make 
holes in the soil or in the bottom of the trench (Fig. 140), and 
rill them with moist, well packed sand. The holes are about 
six inches in diameter and five or six feet deep. 

Concrete may be used alone in the trench, or spread over a 
layer of stones well rammed in place. In either case, the 
concrete is spread in layers and rammed to form one compact 
mass. The upper surface is levelled off, and the foundation 
courses begun as soon as the concrete has set. 

A concrete bed is also used when the soil is all sand ; a 
trench is dug and the concrete laid as just described. 

The pressure allowed on a concrete bed should not exceed 
one tenth part of its resistance to crushing. 

By distributing the weight as nearly as possible uniformly 
over the foundation courses, the dangers of unequal settling 
may be avoided. If the structure rests on piers or other sepa- 
rate supports, these supports should be connected by inverted 
arches, and in this way the weight is distributed over the 
whole bed. If the weight of the structure varies in its differ- 
ent parts the surfaces of the bed should be proportioned 
accordingly, so as to have on each unit of surface the same 
amount of pressure. 



282 CIVIL ENGINEERING. 

380. In compressible soil. — The principal difficulty met 
with in forming a sufficiently firm bed in a compressible soil 
arises from the nature of the soil, its yielding in all directions 
under pressure. There are several methods which have been 
used successfully in soils of this kind. 

One method, when the compressible material is of moder- 
ate depth, is to excavate until a firm soil is reached, and then 
prepare the bed as described in the previous examples. The 
great objection to this method is the expense of excavation, 
especially when the depth of excavation is considerable. 

A second method is to drive piles through the soft soil 
and into the firm soil beneath it. The piles are then cut off 
at a given level, fastened firmly together by heavy timbers, 
and a platform laid upon the top of the piles. On this plat- 
form the foundation courses of the structure rest. 

A third is to use a modification of the last method. In- 
stead of the piles reaching the firm soil, they are only driven 
in the compressible one. The platform is made to extend 
over so large an area that the pressure on the unit of surface 
produced by the weight of the structure is less than the limit 
allowed for this particular soil. 

A fourth is also a modification of the secoud method, and 
differs from the last one in using piles of only five or six 
inches in diameter and five or six feet long. These piles are 
placed as -close together as they can be driven, and support a 
platform, as in the second method. The object of the short 
piles is to compress the soil and make it firmer. 

A fifth is to enclose the area to be covered by the struc- 
ture by sheet-piles. The piles are driven to the firm soil, 
but not necessarily into it. The enclosed area is then covered 
with brush, fascines, or other similar materials, which are 
pressed down into the soft soil. When this upper layer is 
sufficiently firm, the foundation is begun. 

This last method can only be used for small structures of 
a temporary nature. The stability of the construction de- 
pends almost entirely upon the power of the sheet-piles to re- 
sist the pressure transmitted to them by the compressible soil. 

In general, if the firm stratum beneath the compressible 
soil can be reached by piles of ordinary dimensions, the 
second method is the one preferred, especially in those situ- 
ations in which there is no danger of the piles rotting. 

imi.es. 
387. A pile is a large piece of iron or timber, pointed at 



r 



piles. 283 



one end ; it is driven or forced into the earth and used generally 
as a support for some structure. Piles are classified, from 
the material of which they are made, into wooden and 
iron; from their length, into short and long; from the form 
of construction, into round, square, and sheet piles ; and 
from the method used to force them into the earth, into com- 
mon, screw, and pneumatic piles. 

388. Short piles. — These piles are usually round, from six 
to nine inches in diameter, and from six to twelve feet long, 
and made of timber, which may be oak, elm, pine, or other 
suitable wood, the particular kind depending upon the 
abundance of the wood in the vicinity of the work and the 
particular use to which the pile is to be placed. Their cross- 
section is sometimes a square. Their most general use is 
to compress and make firmer the soil in which they are 
driven. 

3S9. Long piles. — These are either round or square in 
cross-section, and have a length of about twenty times their 
mean diameter of cross-section. The diameter of the small 
end should not be less than nine inches. 

They are generally made of timber, the particular kind 
depending upon circumstances similar to those given for the 
short pile. 

The long wooden pile is prepared for driving by having all 
knots and roin?h projections trimmed off, and having the end 
which is to enter the earth sharpened to a point. 

This point should be kept on the axis of the pile, and the 
sharpening, which should extend for a distance equal to once 
and a half or twice the diameter, be symmetrical with respect 
to the same line. 

If the ground into which the pile is to be forced is stony 
or very hard, its lower extremity should be protected by an 
iron shoe. The shoe should be pointed, and may be made of 
cast iron. 

The head of the pile should be protected from the blows 
nsed to force it down. This is usually effected by banding 
the head with a wrought-iron hoop, which is afterwards re- 
moved. Major Whistler's plan was to hollow out the head of 
the pile with an adze, the concavity in the head of the pile 
being made about one inch deep, and then to cover the head 
of the pile with a thin piece of sheet iron. By this means 
the piles were driven without injury. 

As a rule, long piles are used to support a weight placed 
upon them. There are two cases, one in which the pile 
transmits the load to a firm soil, thus acting as a pillar ; the 



284 CIVIL ENGINEERING. 

other is where the pile and the load are wholly supported by 
the friction of the earth on the sides of the pile. 

390. Sheet-piles. — These are flat piles of rectangular cross- 
section, driven side by side in a vertical position, or one that 
is nearly so, to form a sheet. The- use of this sheet is either 
to prevent the materials enclosed by it from spreading out, 
or to protect them from the undermining action of water. 

Sheet-piles are prepared for driving by having their edges 
fitted, so as to ensure a close contact. This is sometimes 
effected by "tonguing and grooving" each pile, but this is 
hardly ever necessary, for if the sides of the piles in contact 
are parallel and the piles well driven, the swelling of the 
wood by the water will ensure a sufficiently tight joint. 

The sheet-piles are kept in position while they are being 
driven by resting them against horizontal pieces firmly bolted 
to guide-piles. The lower end of the sheet-pile is cut with 
an inclined edge for the purpose of giving the pile a drift 
towards the one next to it. 

391. Iron piles. — Short, long, and sheet-piles are fre- 
quently made of iron. In many situations they can be used 
to advantage. It is. not probable, however, that they will ever 
supersede those made of wood. 

The long iron pile, when solid, is made of wrought iron. 
The best form for those of cast iron is tubular. The iron pile 
is forced into the earth either by means of a screw or by the 
pneumatic process. But if forced in by blows on the head, a 
wooden punch must be used with those made of cast iron, to 
avoid the danger of breaking from the blows. 

Sheet-piles of cast iron have been frequently used, especially 
in coffer-dams. They are from fifteen inches to two feet wide, 
half an inch thick, and strengthened generally by flanges or 
vertical ribs. The joints are made tight by having one pile 
to overlap the two adjacent ones. 

The difficulty met with in driving them to the same level 
is a serious objection to their use in many cases. This objec- 
tion does not apply to their use in a coffer-dam, as it is of no 
consequence about having the heads of the piles on the same 
level. 

392. Screw piles. — They are either of wood or iron. Gen- 
erally they are made of iron. The screw blade is ordinarily 
of cast iron, fixed on the foot of the pile, and seldom makes 
more than one turn. The diameter and the pitch of the 
screw vary with the nature of the soil and the load to be sup- 
ported. 

The piles are made either hollow or solid. The hollow 



PILES. 



2S5 



piles are of east iron, from one to three feet in diameter, and 
generally cast in convenient lengths, which are afterwards 
connected together. Fig. 141 shows a cast-iron pile of the 
ordinary kind ; it is about two feet and six inches in diame- 
ter. Solid piles are made of wrought iron, and are from four 
to nine inches in diameter. Fig. 142 shows one with a cast- 
iron screw. 

Screw piles are applicable for use in sand, gravel, clay, soft 
rock, and alluvial soils. They can be forced into very hard 
soils, even into brickwork. To force them into the earth, it 
is usual to fix upon the top of the pile a capstan, and to apply 
the power to the levers which turn it. A strong frame-work 
is needed to hold the pile in its place while it is being screwed 
down. 




Fig. 141. 



Fig. 142. 



Fig. 143. 



393. Disk piles. — These are iron piles with the base en- 
larged by a broad disk attached to the foot (Fig. 143). They 
have been used successfully in light sand. 

To sink them, the top is closed except where a tube of 
small diameter is inserted. Through this small tube, water 
is forced at high pressure by a force-pump, and as it rushes 
out at the base" of the pile, it disturbs the sand, and the pile 
descends by its weight. When it has descended far enough, 
the pumps are stopped, and the sand settling around the pile 
holds it firmly in position. Great caution should be observed 
to settle the foot of the pile some distance below the scour, 
or that point where there is danger of the sand being dis- 
turbed by water or any other cause. 

394. Pneumatic piles. — These are iron cylinders which 
are used instead of common piles to reach a firm stratum 
lying below both water and an overlying bed of soft material, 
like that of a river bed. 

The piles are sunk below this soft material, or rather 



286 CIVIL ENGINEERING. 

through it, either by exhausting the air from the interior of 
the cylinder, thus producing a pressure on the head of the 
pile, or by forcing air in the tube, driving the water out, so 
that workmen are able to descend to the bottom of the pile 
and remove any obstructions to its settling. The details of 
this method will be given in another article. 

395. Means used to force common piles into the earth. 
— Short, long, and sheet-piles of wood are forced into the earth 
most generally by blows delivered on their heads. The 
machines used to force them into the ground are called " pile- 
drivers,'' and are of various kinds. The one most commonly 
used consists essentially of a large block of iron which slides 
between two uprights, termed guides or leaders. This block, 
called the ram or monkey, having been drawn to the top 
of the guides, is let fall and comes down on the head of the 
pile with a violent blow, forcing the pile into the soil. 

The pile-driver may be worked by hand, horse, or steam 
power. 

The simplest form of pile-driver is the ringing engine. 
In this machine the ram is attached to one end of a rope 
which passes over a pulley, the other end of it branching 
out into a number of smaller ropes, each held by a man. 
"The men, all pulling together, lift the ram a few feet, and at a 
given signal all let go, allowing the ram to fall on the pile. 
The number of men required will depend upon the weight of 
the ram. It is usual to allow about forty pounds to each 
man. 

In the machine commonly used, the ram is raised by the 
power being applied to a windlass. The ram is held while 
being hoisted by tongs or nippers, the handles of which, 
when the ram has been raised to the proper height, come in 
contact with two inclined planes on the guides, which press 
the handles of the tongs together, opening the tongs and 
letting the ram fall. The tongs are so arranged that upon 
being lowered they catch hold of the ram by a staple or 
other contrivance on its upper surface. 

If the piles are to be driven in an inclined position, it is 
only necessary to incline the guides. As a rule, the direc- 
tion of the pile should be parallel to the pressure it has to 
support. 

396. Other machines are frequently used to drive piles. 
The most important one is an application of the steam ham- 
mer. In this driver, the hammer is attached to a piston-rod 
passing out of a cylinder fixed on the top of a wrought-iron 
case which moves between the guides. 



PILE-DRIVING. 287 

It is well adapted for continuous rows of piles, and can be 
economically used where there are a great number to be 
driven, and where the piles are near each other. 

In the ordinary machine, the pile is driven by a compara- 
tively small mass descending from a considerable height with 
great velocity. But with the steam hammer, the pile is 
forced into the earth by the blows of a heavy mass, delivered 
rapidly upon a block weighing several tons, placed directly 
over the head of the pile. The blows are given at the rate of 
one a second by a heavy hammer raised a height equal only 
to the stroke of the piston. 

Various methods have been used in different machines to 
raise the ram. In some cases the pressure of the atmosphere 
has been tried with success. In one machine the explosive 
properties of gunpowder are the means used. • 

397. If the head of a pile has to be driven below the level 
to which the ram decends, another pile, termed a punch, is 
used for the purpose. A cast-iron socket of a suitable form 
embraces the head of the pile and the foot of the punch, 
and the effect of the blow is thus transmitted through the 
punch to the pile. 

The manner of driving piles, and the extent to which they 
may be forced into the subsoil, will depend on local circum- 
stances. It sometimes happens that a heavy blow will effect 
less than several slighter blows, and that piles, after an inter- 
val between successive volleys of blows, can wjth difficulty 
be started at first. They may be driven in rocky soils and 
even in rock itself, if holes are first made whose diameters are 
little less than those of the piles. They should in this case be 
shod with an iron shoe. Careful attention is required iii driv- 
ing, for a pile has been known to break below the surface 
and to continue to yield under the blows of the ram by the 
crushing of the fibres of the lower end. 

The test of a pile having been sufficiently driven, according 
to the best authorities, is that it shall not sink more than 
one-fifth of an inch by thirty blows of a ram weighing 800 
poinds, falling five feet at each blow. A more common rule 
is to consider the pile full)- driven when it. does not sink more 
than one-fourth of an inch at the last blow of a ram weigh- 
ing 2,500 pounds, falling 30 feet. 

The least distance apart that piles cam be driven with ease 
is about two and one half feet between their centres. If they 
are nearer than this, they force each other up as they are 
driven. The average distance is generally about three feet. 

If a pile has to be drawn out, as is often the case, a lever 



288 CIVIL ENGINEERING. 

fastened to it by a chain around the head, with one end rested 
on a firm point of support and the other end raised by the 
power used in the pile driver, will ordinarily effect it. Where 
the pile is only partially driven, it may sometimes be drawn 
out by fastening a chain around the head of the pile and seiz- 
ing it with the nippers. 

39S. Load on piles. — The rule in practice, for a safe load 
on piles, is to allow in the case of the pile transmitting the 
weight to a firm soil, 1,000 pounds on the square inch of the 
head ; where they resist wholly by friction on the sides, one- 
fifth of this, or 200 pounds. Captain Sanders' rule was ex- 
pressed by the formula, W = -JR x -y, in which W is the 

Co 

safe load, R, the weight of the ram, both in pounds ; h the dis- 
tance of the fall of the ram, and d the penetration, both in feet. 

399. Preparation of bed in compressible soil, using 
common wooden piles. — The piles are used to transmit the 
pressure to the firm soil beneath. 

The piles having been driven, their heads are sawed off at 
a given level and the whole system is firmly connected to- 
gether by longitudinal and cross pieces notched into each 
other and bolted to the piles. On these piles a platform is 
laid or the soft earth around the top of the piles is scooped 
out for five or six feet in depth, and this space filled with 
concrete. 

If a platform is to be used, it is constructed as follows : 
A large beam, called a capping, is first placed on the heads 
of the outside rows of piles and fastened to them by iron 
bolts, or wooden pins termed treenails. Sometimes an occa- 
sional tenon is made on the piles, fitting into a corresponding 
mortise in the capping. Other beams are then laid resting 
on the heads of the intermediate piles, their extremities resting 
on the cappings, and are then bolted firmly to the piles 
and the cappings. At right angles to these, another set of 
beams are laid and bolted to the piles. Where the beams 
cross each other, they are both notched so as to have their 
upper surfaces in the same plane. The beams which have 
their lengths in the direction of the longer sides of the struc- 
ture are known as string pieces, and those at right augles to 
these are termed cross pieces. 

Upon the upper surface of the beams a platform of thick 
planks is laid and spiked to them. 

The cappings are sometimes of larger size than the others, 
in which case a rabbet is made in the inner edge so as to have 
the platform flush with the upper surface of the capping. 



GRILLAGE AND PLATFORM. 



289 



The whole construction is called a grillage and platform. 
(Fig. 144.) 




Fig. 144 — Represents a grillage 
and platform fitted on piles. 
A, masonry. 
<7, a, piles. 
&, string pieces. 
6, cross pieces, 
rf, capping piece, 
e. platform of plank. 
/, concrete. 
#, soft soil. 
A, firm soil. 



400. "When the firm stratum into which the piles have been 
driven underlies a soil so soft that there is doubt of the lateral 
stability of the piles, the soft soil should be scooped away and 
stones thrown between and around them to increase their 
stiffness and stability. (Fig. 145.) 




Fig. 145 — Represents the manner of 
using loose stone to sustain piles and 
prevent them from yielding laterally. 

A, section of the masonry. 

B, loose stone thrown around the piles. 



401. If the situation be such that decay in the timber is to 
be expected, the more costly method of excavation must be 
adopted. 

The practical difficulty met when trenching in such cases, is 
19 



ft vr 



290 CIVIL ENGINEERING. 

the presence of water in such quantities as to seriously. impede 
the workmen, even to the extent often of failure. 

Pumps are used to keep the water out, and it may even be 
necessary to enclose the entire area by a sheet-piling. In 
which case, two rows of sheet-piles are driven on each side of 
the space to be enclosed, through the soft material and into 
the firm stratum beneath. The soft material between the rows 
is then scooped out, and its place filled with a clay puddling, 
forming a water-tight dam around the space enclosed. If the 
water comes from springs beneath the dam or from within 
the area enclosed, this method will fail, and it may be neces- 
sary in that case to resort to some of the methods used for 
laying foundations under water. 



CHAPTER XII. 

FOUNDATIONS IN WATER. 



402. Two practical difficulties meet the engineer in pre- 
paring beds of foundations under water.- One is to make the 
necessary arrangements to enable the workmen to prepare 
the bed ; and the second, having prepared the bed, to secure 
it against the deteriorating effects of the water and preserve 
its stability. 

Preparation of the bed. — There are two general cases 
under which the bed is prepared : one is where it may be 
prepared without excluding the water from the place it is to 
occupy ; and the other is where the water must be excluded 
from the area to be occupied before the bed can be made. 



PREPARATION OF BED WITHOUT EXCLUDING THE WATER. 

403. Concrete beds. — A bed of concrete is frequently used 
in this case. To prepare the bed, the upper layer of loose, 
soft soil is removed by a dredging-machine or other means, 
and the site made practically level. In this excavation the 
concrete is laid. To do this, a conduit made of wood or iron, 
or a box or contrivance which opens at the bottom when 
lowered in position, may be used. 



FOUNDATIONS IN WATER. 



291 



A cylindrical conduit of boiler iron, made in sections of 
suitable lengths which can be successively fastened on or 
detached as the case requires, has been used with success. 
The lower end of the conduit has the form of a frustum of a 
cone. The whole arrangement is lowered or raised at pleas- 
ure by means of a crane. The concrete, being placed in the 
conduit at the upper end, by a proper motion of the crane is 
spread in layers as it escapes from the lower end. By lifting 
and dropping the apparatus the layers can be compressed. 

Ba<j;s rilled with concrete have been used, with a moderate 
degree of success, for the same purpose. 




Fig. 146. 



The object to be attained is to get the concrete placed in 
position as nearly as possible in the same condition as when it 



292 CIVIL ENGINEERING. 

is made. If it be allowed to fall some distance through water, 
or placed in a strong current, the ingredients of the concrete 
are liable to be separated. 

Where the site is in flowing water, it is often necessary 
to provide some arrangement which enclosing the area will 
cause the water within the enclosure to be still and prevent 
its injurious effect upon the fresh concrete before it has set. 

404. The arrangement shown in Figure 146 was used for this 
purpose. It consisted of a framework composed of uprights 
connected together by longitudinal pieces in pairs ; each pair 
being notched on and bolted to the uprights, leaving an interval 
through which sheet-piles were inserted. The sheet-piles 
were driven into close contact with the bottom, which was 
rock. The frame was*put together on the shore and then 
floated to its place. It was secured in position by inserting 
the uprights in holes drilled in the rock. The -sheet-piles 
6', 6 ', were then inserted between the horizontal pieces b, V , 
and rested oh the bottom. The whole area was thus en- 
closed by a wooden dam, within which the water was cpiiet. 
The concrete was then laid on the bottom of the enclosed 
space. To prevent the sides of the dam from spreading out 
iron rods d, d< d', d\ were used to connect them. * 

405. Beds made of piles. — Common wooden piles are fre- 
quently used to form a bed for the foundation courses of a 
structure. They are driven through the soft soil into the 
firm stratum beneath, and are then sawed off on a level at or 
near the bottom. On these are laid a grillage and platform 
or other suitable arrangement to receive the lower courses. 
"Where the bottom is suitable for driving piles, and tlrere is 
no danger of scour to injure their stability, this method is 
economical and efficient. The foundation courses must be 
placed in position by some submarine process, as a diving- 
bell, or by means of a caisson. 

406. Common caisson. — This caisson (Fig. 147) is a water- 
tight box, whose sides are ordinarily vertical, and capable of 
being detached after the caisson has been sunk in position. 
The bottom of the caisson, forming a part of the foundation 
of the structure, is made of heavy timbers, and conforms in 
its construction to that of a grillage and platform. 

The size of the timbers for the bottom is determined by the 
weight of the structure which is to rest on them, and for the 
sides, upon the amount of pressure from the water when the 
caisson rests on its bed. 

The sides arc; generally made of scantling, covered with 
thick plank. The lower ends of the scantling or uprights tit 



CAISSONS. 



293 



into shallow mortises made in the cap pieces of the grillage. 
]>eams are laid across the top of the caisson, notched upon the 
sides and projecting beyond them. These cross pieces are 
connected with the lower beams of the grillage by long iron 
bolts, which have a hook and eye joint at the lower end and a 
nut and screw at the upper. By unscrewing the bolts at the 
top, they can be unhooked at the bottom, the cross beams 
raised, and the sides of the caisson detached. 



FrG. 147 — Represents a cross- 
section and interior end 
view of a caisf-on. The 
boards are let into grooves 
in the vertical pieces in- 
stead of being- nailed to 
them on the exterior. 

a, bottom beams let into 
grooves in the capping. 

b, square uprights to sustain 
the boards. 

c, cross pieces resting on b. 

d, iron rods fitted to hooks at 
bottom and nuts at top. 

e, longitudinal beams to stay 
the cros« pieces c. 

A, section of the masonry. 

B, bed made of piles. 
/', guide piles. 




In a caisson which was used in building a bridge pier, the 
exterior dimensions of the principal parts were nearly as fol- 
lows : 

The caisson was 63 feet long, 21 feet wide, and 15 feet 
deep. The cross beams on top were made 10 inches square 
in cross-section, and were placed about three feet apart ; the 
uprights were of the same size as the cross pieces, and were 
placed about six feet apart. 

Much larger caissons have been used, especially in some of 
the engineering constructions in England. 

The caisson is built at some convenient place where it can 
be launched and towed to the position it has to occupy. The 
bed having been prepared by levelling off the bottom or mak- 
ing one of piles, the caisson is floated to and moored over the 
spot. The masonry courses are then laid on the bottom of 
the caisson, and are built up until the caisson rests on its bed. 
Just before it reaches the bed, it is sometimes settled in place, 



294 CIVIL ENGINEERING. 

by admitting water into the interior, and an examination 
made as to its proper position. If it does not occupy its 
proper place, and there is a desire to change the position of 
the caisson, the gates by which the water was admitted are 
shut and the water pumped out. The removal of the water 
will allow it to float and a rectification of its position may 
then be effected. 

The caisson having been satisfactorily settled in position, 
the masonry is built above the surface of the water, and the 
sides are detached and removed. 

Caissons are frequently used whose sides are not detached. 
This is especially the case where the sides are of a permanent 
character. These might be termed permanent caissons. 

407. Permanent caissons.— Caissons built- with brick 
sides and timber bottoms were used to construct the sea-wall 
at-Sheerness, in England, in 1811-12. After being sunk, they 
were filled with concrete. 

Rankine mentions a kind that are built wholly of bricks 
and cement, which after being sunk in place are filled with 
concrete. 

40S. Diving apparatus. — Another method of preparing 
the bed, is to use some apparatus which will admit of the 
workmen executing their labors notwithstanding the presence 
of the water. Submarine or diving armor and diving-bells are 
devices which are frequently used for this purpose. 

I. Submarine armor. — This is an apparatus to be used by 
a single person, and consists essentially of a metallic helmet 
enclosing the man's head. It rests upon his shoulders and is 
connected with a dress worn by him which is air and water- 
tight, lie is supplied with fresh air forced through a flexible 
tube which enters at the back of the helmet ; a valve opening 
outwards allows the foul air to escape. To enable him to 
see, the helmet is provided with eye-holes protected by strong 



II. Diving-bell. — The form of diving-bell, commonly used, 
is that of a rectangular box with rounded corners. Holes 
protected by strong glass about two inches thick are made in 
the top to admit light into the interior. Fresh air is forced 
through a flexible tube into the bell by means of air-pumps. 
The bell is raised and lowered by means of a crane and 
windlass. 

A bell, whose dimensions are four feet wide, six feel long, 
and five feet high on the inside, forms a convenient size for 
laying masonry under water. 

The diving-bell has been much used in laving submarine 



WELL FOUNDATIONS. 295 

foundations where there was no scour and where the bed was 
easily prepared. 

400. Pierre perdue. — The methods just given are appli- 
cable to structures of moderate dimensions. When the area 
occupied by the bed is very considerable, these methods are 
not applicable or require modifications. The one known by 
the French as pierre perdue has been frequently used. It 
consists of forming an artificial island of masses of loose stone 
thrown into the water, and letting them arrange themselves. 
This mass is carried up several feet above the surface of the 
water and the foundations built upon it. 

The structure should not be commenced until the bed has 
fully settled. If there is any doubt about this, the bed should 
be loaded with a trial weight, at least twice as great as that of 
the proposed structure. 

This method can not be vised in navigable rivers or other 
situations where it is of greater importance not to contract 
the water-way. 

410. Screw piles. — Iron screw piles have been used with 
success for foundations in localities where the methods already 
mentioned were not practicable. They do not differ, in prin- 
ciple, from the common wooden pile. When using the latter, 
it is necessary for its preservation that the pile should be 
entirely submerged, which is not necessary for the iron one. 
The wooden one could not be relied on in saltwater. 

Iron screw piles have been much used, in the United States, 
in the construction of light-houses on or near sandspits at the 
entrance of our harbors and on shoal spots off the coast, where 
it would be almost impossible to prepare the beds by any of 
the other more usual methods. 

411. Well foundations, — In India, a method known as 
well or block foundations has been quite extensively used, 
especially in deep sandy soils. The method consists in sink- 
ing a number of wells close together, filling them with 
masonry, and connecting them together at top. 

The method of sinking one of the wells is to construct a 
wooden curb about a foot in thickness and with a diameter 
of the same size as that of the well, and place it in position 
on the proposed site. On this curb a cylinder of brickwork 
is built to a height of about four feet. As soon as the mortar 
has set, the sand is scooped out from under the curb, ;md it 
descends, carrying with it the masonry. When it has settled 
as far as it is desired, another block or height of masonry is 
added, and again the sand is scooped out from under the 
curb, and the whole mass descends as before. This process 



296 CIVIL ENGINEERING. 

is then repeated and carried on until the curb has readied 
the required depth. Care must be taken to regulate the 
excavation so that the cylinder shall sink vertically. 

From the very nature of the soil, water is soon met, and 
is kept out either by bailing or by pumping. As loug as 
this can be done the work proceeds with rapidity. If the 
water comes in so fast that it cannot be exhausted by these 
means, the sand must be scooped out by the use of contriv- 
ances of some kind, or by means of divers. Under these 
circumstances the excavation proceeds slowly and with diffi- 
culty. 

When the curb reaches a firm stratum, or a depth where 
there is no danger of the foundations being affected by the 
water, the bottom is levelled, a concrete bed made, and the 
interior of the cylinder filled in solid with masonry. If the 
concrete bed is made without exhausting the water, this is 
pumped out as soon as the concrete sets, and the masonry is 
built in the usual manner. 

Cylinders of boiler iron have been used in the same way, 
and are an improvement upon the masonry curbs. 

412. Iron tubular foundations. — This is a general name 
applied to large iron cylinders which are sunk through water 
and a soft bottom to a firm soil, and used to support a given 
structure in the same manner as common piles. The num- 
ber and size of them depend upon the weight to be supported 
and the means adopted to sink them. 

The method just described for the wells is frequently used 
for the iron tubes. Brunei, the English engineer, in building 
the Windsor Bridge, on the Windsor branch of the Great 
Western Railway, employed this method in constructing the 
abutments of the bridge. There were six cast-iron cylinders, 
each six feet in diameter, in each abutment, which were 
sunk to the proper depth by excavating the earth and gravel 
from the interior with dredges and forcing the cylinders 
down by weights placed on the top of each one. 

The concrete bed in the bottom was made by lowering the 
concrete to the bottom in bags, which were arranged so that by 
pulling a rope the bags were emptied under the water in the 
proper place. When a sufficient quantity had been put in 
and had hardened, the water was pumped out and the cylin- 
ders filled in the usual manner. 

This method does not differ in principle from a. foundation 
on piles, and the same general rules apply as to the amount of 
load to be supported and the depth to which the pile is to be 
driven. 



COFFER-DAMS. 297 

In some cases a clump of common piles was driven within 
the cylinder at the bottom, and the spaces between them filled 
with concrete. The piles extend in some of the recent con- 
structions to the top of the cylinder. 



I PREPARATION OF BED, THE WATER BEING EXCLUDED. 

413. There are two cases : where the water is excluded by 
means of a dam, and where it is excluded by atmospheric 
pressure. 

I. EXCLUSION OF WATER BY DAMS. 

The dams used are the common earthen or clay dam, the 
common coffer-dam, and modified forms of the coffer-dam. 

414. Earthen dam. — In still water not more than four 
feet deep, a dam made of earth or ordinary clay is usually 
adopted to enclose the given area* and to keep out the sur- 
rounding water. It is made by digging a trench around the 
area to be enclosed and removing the soft material taken out. 
The earth or clay is then dumped along the line of this 
trench until it rises one or two feet above the surface of the 
water. As the earth is dumped in place it should be firmly 
pressed down and when practicable, rammed in layers. Any 
good binding earth or loam will be a suitable material for the 
dam. 

The dam being finished, the water within the enclosed 
area is pumped out, and the bed and foundations constructed 
as already prescribed for those "on land." 

415. Coffer-dam. — Where the water is more than four feet 
deep and especially if it be running water, the common 
earthen dam would be generally too expensive a structure, 
even if it could be built. In a case of this kind, and where 
the water does not exceed twenty -live feet in depth, the com- 
mon coffer-dam is usually employed. 

The common coffer-dam (Fig. 148) is essentially a clay 
dam, whose sides are vertical and retained in position by two 
rows of piling. 

The common method of constructing the coffer-dam is to 
drive two parallel rows of common piles around the area to 
be enclosed ; the distance between the rows being equal to 
the required thickness of the dam, and the piles in each row 
from four to six feet aj3art. 

The piles of each row are then connected by horizontal 



298 



CIVIL ENGINEERING. 



beams, called string or wale pieces, which are notched on 
and bolted to the piles on the outside of each row, and about 
one foot above the highest water mark. On the inside of the 
rows, and nearly opposite to the wale pieces, are placed string 
pieces of about half the size, which serve as guides and sup- 
ports to the sheet piles. 




Fig. 148-Represents 
a section of a 
coffer-dam. 

a, common piles. 
If 6, wale or string 
pieces 

c, cross pieces. 

d, sheet piles. 
4, puddling. 

B, mud and loose 
soil. 

C, firm soil. 



The two rows of piles are tied together by cross pieces 
notched on and bolted to the outer wale pieces. Upon these 
cr ss pieces are laid planks to form a scaffolding for the 
workmen and their tools, etc. 

The sheet-piles are driven in juxtaposition through the soft 
soil and in contact with the firm soil beneath. They are 
about four inches thick and nine inches wide, and are spiked 
to the inner string pieces. Sometimes an additional piece, 
known as a ribbon piece, is spiked over the sheet-piles. 

These rows of sheet-piles form a coffer for the puddling, 
whence the name of the construction. The sheet-piles having 
been driven and secured to the string pieces, the mud and 
soft material between the rows are scooped or dredged out. 

The puddling which forme the dam is then thrown in and 
pressed compactly in place, care being taken to disturb the 
water as Little as possible during the operation. When the 
top of the puddling rises to its required height, pumps are 
used to exhaust the water from the enclosed area. The in- 
terior spaee being free from water, the bed of the foundation 
is prepared as if it were on dvy land. 

The puddling is composed of clay mixed with sand or 



COFFER-DAMS. 299 

gravel, o r of fine g ravel alone, freed from all large stones, 
roots, or foreign -material wliich may be mixed with it. The 
clay is worked into a plastic condition with a moderate 
amount of water, and then mixed thoroughly with a given 
quantity of sand or fine gravel. Care is taken that there are 
no lumps in the puddling after the mixing. 

The required thickness to give the dam is obtained ordi- 
narily by making it equal to the height of the dam above the 
ground or bottom on which it is to rest, when this height does 
not exceed ten feet. For heights greater than this, the rule 
is to add to ten, one foot for every additional height of three 
feet. 

This gives a greater thickness than is necessary to make the 
dam water-tight, but adds to its stability. The stability of 
the dam is sometimes still further increased by supporting 
the sides of the dam by inclined struts, the upper ends of 
which abut against the inner row of common piles, and the 
lower ends against piles driven for that purpose into the 
ground. 

416. The principal difficulties met with in constructing a 
coffer-dam are as follows : 

First, To obtain a firm hold for the common piles ; a dif- 
ficult thing to do in deep muddy or rocky bottoms ; 

/Second, To prevent leakage between the surface of the 
ground and the bottom of the puddling ; 

Third, To prevent leakage through the puddling; 

Fourth^ To exhaust the water from the enclosed area after 
the dam is finished. 

These difficulties and the expense of construction of the 
dam, increase very greatly with the depth of the water. In 
deep water, the size aud length of the piles and the amount 
of bracing required to resist the pressure of the water render 
the expense very great. 

Common piles can not be efficiently used where the bottom 
is rocky. In a case of this kind, the following construction 
was successfully used : 

Instead of the common piles, two rows of iron rods were 
used. These rods were "jumped" into the rock, a depth of 
fifteen inches. The sheet-piles were replaced by heavy planks 
which were laid in a horizontal position and fastened to the 
rods by iron rings. This method of fastening allowed the 
planks to be pushed down until each one rested on the one 
below it ; the plank resting on the bottom beiug cut to fit the 
surface of the rock. 

The frame was strengthened by bolting string pieces of 



300 CIVIL ENGINEERING. 

timber in pairs on both sides and using inclined struts upon 
the interior. 

The puddling was of the usual kind and put in the dam in 
the way already described. 

417. It will be very difficult to avoid leakage between the 
bottom of the puddling and the soil on which it rests if the 
stratum of overlying soft soil be not removed. It is therefore 
recommended for important works that a part of the dredging 
for this purpose be clone before the common piles are driven. 

Leakage through the puddling is mostly due to poor work- 
manship. If the sheet-piles are fitted and carefully driven, 
and the puddling is free from lumps and thoroughly mixed, 
leakage through the dam may be prevented. It is not advis- 
able to have bolts or rods passing through the dam, as leakage 
almost invariably takes place through the holes they make. 
Eine gravel alone has been proved a better material for the 
filling than ordinary puddling. 

Leakage due to springs in the bottom of an enclosed area 
is the great source of trouble, and in some soils is stopped 
with much difficulty. It may be necessary to fill in the whole 
area with a bed of concrete, and after it has set to pump out 
the water. 

418. The water having been pumped out, the enclosed 
space is drained into some conveuient spot in the enclosure, 
and arrangements made to keep the interior dry. The bed 
having been prepared, the masonry is then built to the proper 
height. When it is above the surface of the water, the dam 
may be removed, and as there is danger of disturbing the bed 
if the piles were drawn out, it is customary to cut them oft' at 
some point below the water line, letting the lower ends 
remain as driven. 

419. Caisson dams. — This name was given to a coffer-dam 
in which the outer row of common piles was replaced by 
structures resembling caissons, which were sunk and ballasted 
to keep them in position along the line which would have 
been occupied by the common piles. 

The character of the bottom and the nature of the stream 
were such that common piles for the dam could not be used. 

The caisson (Fig. 149) was a fiat-bottomed boat, which hav- 
ing been floated to its place was sunk gradually, by the ad- 
mission of water, until it rested on the bottom. Two rows of 
common piles were then lowered and kept in a vertical posi- 
tion on each side of the caisson until they rested on the bot- 
tom. They were then»bolted in that position to the sides of 
the caisson. The caisson was then heavily loaded with stones 



CAISSON DAMS. 



301 



ami other weighty materials, until a considerable weight rested 
on the piles. It is observed, that instead of the piles being 
held fast by being driven into the ground, they are held in 
place by the sunken boat, and the whole arrangement takes 
the place of the outer row of piles in the common coffer-dam. 



% 




i 




f 


\ H_^_ 




-' 1 


: V 


; I 


Willi 


b 1 -V^ 


■ 1 


| S3 








FlS. 149 — Represents a cross-section of a caisson dam. 
A, cross-section of caisson. C, puddling-. 

D, foundation courses of the pier. 



To complete the dam, a row of posts, parallel to the inner 
row of piles, resting on the bottom and connected by a frame- 
work with the caissons, took the place of the inner row of 
piles in the common coffer-dam. 

The sheet-piles were required only on the one side, the 
sides of the caissons being sufficient on the other. They were 
laid in a horizontal position, as shown in the figure. The 
puddling was in all respects the same as that described in the 
previous cases. 

The masonry being finished, the loads were removed from 
the caissons. They were then pumped dry and the dam re- 
moved. 

420. Crib-work dam. — A dam in which a crib ballasted 
with stone takes the place of the common piles, has been used' 
with success. 

In the example (Fig. 150), the cribs were built by laying 
the log's alternately lengthwise and crosswise*, and fastening 
them together at their intersections by notching one into the 
other and pinning them. 



302 



CIVIL ENGINEERING. 



On eacli crib a platform was laid about midway between 
the top and bottom, on which the stone^was placed to sink the 
crib. The cribs were floated to the place they were to occupy 
and sunk gradually by loading stone on the platform. When 
they had been fully settled in their place, more stones were 
piled on until its stability was secured. 




Fig. 150 — Represents a cross-section of a crib-work dam. 

A, inner row of cribs. B, outer row of cribs. C, puddling-. 

Both of the preceding methods were used in constructing 
the piers and abutments of the Victoria Bridge, over the 
Saint Lawrence, at Montreal. A rocky bottom, covered with 
boulders, prevented the use of the common pile by the ordi- 
nary method of driving them. There was also in the river a 
swift current, which in the spring of the year brought down 
large quantities of ice, the effect of which would have been 
to have destroyed any ordinary caisson or common coffer-dam. 

It is seen that these dams do not differ in principle from 
the common coffer-dam, and that the modifications in each 
case consisted in finding a substitute for the common pile 
which would be stronger and equally as effective. 



II. EXCLUSION OE WATER FROM THE SITE BY ATMOSPHERIC 
PRESSURE. 



421. In recent years, the use of compressed air as a means 
to exclude the water from the site of a proposed work, while 
the bed was being prepared, has been extensively adopted. 

There are two general methods in its application: the 
pneumatic pile and the pneumatic caisson. 

422. Pneumatic piles. — Pneumatic piles are hollow verti- 
cal cylinders or cast iron, from six to fen feet in diameter, 
which are forced through the soft and compressible materials 
forming the bottom to 



a firm soil beneath, and then filled 



PNEUMATIC PILES. 



303 



with masonry or concrete to the top. Itankine classes them 
under the head of iron tubular foundations. 

Their general construction and the mode of sinking them 



in the soil are shown in Fig. 151. 



Fig. 151 -Represents vertical sec- 
tion of a pneumatic pile. 

A, body of cylinder. 

B, the bell. 

C, elevation of air-lock. 

D, vertical section of air-lock. 

E, water discharge pipe. 
M, windlass on inside. 
N, windlass on the top. 

0,0, buckets ascendirg and de- 
scending. 
W,W, iron weights. 




In this example, shown in the figure, the cylinders were 
cast into lengths of nine or ten feet, with flanges on the in- 
terior at each end. These pieces were united by screw bolts 
passing through holes in the flanges, the joints being made 
water-tight either by an india-rubber packing or by a cement 
made of iron turnings. 

To sink a pile of this kind, a strong scaffolding is erected 
over the site, from which the lengths of the cylinders can be 
lowered and placed in position. On this scaffold a steam-en- 
gine is ordinarily placed, which furnishes the power required 
during the operation. 

The lower edge of the lowest section of the cylinder is 
sharpened so that it may sink more easily through the soil. 



304 CIVIL ENGINEERING. 

The upper section, termed the "bell," is usually made of 
boiler iron, with a dome'-shaped or flat top. An " air-lock " is 
used to pass the men and materials in and out of the cylinder. 
In this example there were two air-locks, which were placed 
in the top of the bell, as shown in the figure. Each lock had 
at the top a trap door which opened downwards, and at the 
side a door which opened into the interior of the pile. Stop- 
cocks were provided in each, which communicated with the 
external air and the interior of the pile, respectively ; they 
could be opened or closed by persons inside the tube, within 
the lock, or on the outside. 

The bell was provided with a supply pipe for admission of 
compressed air, a pressure gauge, a safety valve, a large escape 
valve for discharging the compressed air suddenly when 
necessary, and a water-discharge pipe about two or three 
inches in diameter. 

Windlasses placed within the cylinder and on the outside, 
as seen in the figure, were used to hoist the buckets employed 
in the excavation 

The first operation in sinking the pile was to lower the 
lowest section with as many additional lengths united to it as 
were necessary to keep the top of the cylinder two or three 
feet above the surface of the water, until it rested on the 
bottom. The bell and one additional length were then bolted 
to the top of the pile. 

The weight of the mass forced it a certain distance into 
the soil at the bottom of the river, dependent upon the ma- 
terial of which it was composed. As soon as it stopped sink- 
ing, the air was forced in by means of air-pumps worked by 
the steam-engine, until all the water in the tube was expelled. 
Workmen, with the proper tools, were then passed into the 
cylinder by means of the air-locks. 

This was done by the men entering the lock, closing all 
communications with the external air, and then opening the 
srop-cock communicating with the interior of the pile, in a 
few minutes the compressed air filled the lock, and the side 
door was opened, affording an entrance into the interior. To 
pass out it was only necessary to reverse this operation. 

The gearing of the hoisting apparatus was so arranged thai 
the buckets, when filled, were delivered alternately into the 
locks, and were then hoisted out by the windlass on the out- 
Bide. 

Care was taken to guard against the uplifting force of the 
compressed air within the pile. In this example, a heavy 
wciirht, composed of east-iron bars resting on brackets 



■©" u > 



compoi 



PNEUMATIC PILES. * 305 

attached to the outside of the bell, was used to resist this 
action. 

The workmen having descended to the bottom of the pile, 
excavated the material to the lower edge, they then took off 
the lowest joint of the water discharge pipe and carried it 
and their tools to the bell, and they passed out of the lock. 
The valve for admitting compressed air was then closed and 
the large escape valve opened, allowing the compressed air to 
escape. The cylinder being deprived of the support arising 
from the compressed air, sank several feet into the soil, the 
distance depending on the resistance offered b}- the soil. 

When the pile had stopped sinking, the escape valve was 
closed, the air forced in, and the operations just described 
continued. Great care was taken to keep the pile while sink- 
ing in a vertical position. 

The pile, having reached the required depth, was then filled 
with concrete. 

The usual method of filling the pile is to perform about 
one-half of the work in the compressed air and then remove 
the bell and complete the rest in the open air. In filling with 
concrete, it should be well rammed under the flanges and 
around the joints. 

423. This example of a pneumatic pile, just alluded to, is 
that of one of the piles used in the construction of a bridge 
over the river Theiss, at Szegedin, in Hungary. 

The river, at this point, has a sluggish current with a gra- 
dual rise and fall of the water, the difference between the 
highest and lowest stages of water being about twenty-six 
feet. The soil of the bottom is alluvial, composed of alternate 
strata of compact clay and sand, to a great depth. 

The piles were sunk about thirty feet below the bottom of 
the river, which was about ten feet deep at low water. 

The excavation was carried down to within six feet of the 
bottom of the pile. Twelve common piles of pine were then 
driven within the cylinder, extending to a depth of twenty 
feet below it. The concrete was then thrown in and rammed 
hi layers until its upper surface was on a level with that of 
ordinary low water. 

The air-locks were about, six feet and a half high and two 
and three-quarters in diameter. 

424. In the first uses of the pneumatic piles, the cylinders 
were of small size, as many being sunk as were required to 
support the load, as in the case of common piles. 

They were sunk into the soil by exhausting the air from 
the interior. The result following this removal of the air was 
20 



n<r 



306 | CIVIL ENGINEERING. 

to force up with the water into the inside the earth imme 
diately under the cylinder, and the pile sank into the openi 
thus made, both by its own weight and the pressure of the 
atmosphere. 

This process is known as Dr. Pott's, and is well adapted to 
soft or sandy soils, when free from stones, roots, pieces of tim- 
ber, etc. The presence of any obstacle in the soil which the 
edge of the tube cannot cut through or force aside, renders 
impracticable this method of sinking the pile. 

The next step was to increase the size of the pile, and in- 
stead of exhausting the air, to till it with compressed air. 
The top being closed and the bottom open, all fluid matter 
was driven from the interior of the pile by the compressed 
air. By means of air-locks on the top of the cylinder, work- 
men were enabled to descend and remove the soil and such 
obstructions as prevented the pile from sinking. This pro- 
cess is generally known as " Triger's." 

The air being compressed in the interior of the pile, the 
weight or the pressure downward was much lessened. This 
was corrected by using a weight placed on the pile. 

Although many improvements have been made in the de- 
tails, the arrangements just described illustrate the general 
outline of all the pneumatic methods in use. 

425. Pneumatic method used by Mr. Brunei. — The first 
improvement in the pneumatic method was that used by Mr. 
Brunei in preparing the bed and erecting the centre pier of 
the Royal Albert Bridge, at Saltash, England. 

This improvement consisted in confining the compressed 
air to a chamber at the bottom of the cylinder, which was 
connected with air-locks at the top by a tube six feet in dia- 
meter, the rest of the space inside of the cylinder being open 
to the air. (Fig. 152.) 

A dome was built in the lower portion, about 25 feet from 
the bottom, so as to have it above the mud when the cylinder 
rested on the rock. 

A tube ten feet in diameter connected the centre of the 
dome with the top. The chamber for the compressed air was 
an annular one, four feet wide, twenty feet high, built around 
the inner circumference of the lower edge and divided into 
eleven compartments by vertical, and radial partitions; aper- 
tures in the partitions afforded communications from one to 
the other. An air passage at the top of the compartments 
connected them with the vertical tube six feet in diameter, 
which extended to the top of the cylinder and contained the 
air-locks. 



TNEUMATIC TILES. 



307 



The cylinder was lowered into the water exactly over the 
place it was to occupy. As soon as it stopped sinking, the 
annular chamber was shut off from the rest of the dome, the 
air forced in, the water driven out, the workmen descended 
and dug out the mud and loose soil under the edge. 



Fig. 152— Represents a longitudinal section 
through the axis of the cylinder. The 
cylinder was 37 feet in diameter, about 
100 feet high, made of boiler iron, and 
weighed nearly 300 tons. The rock on 
which it was to rest was about 90 feet 
below the surface of the water, overlaid 
with about 20 feet of loose sand and mud. 
The rock surface had a slight slope and 
the bottom of the cylinder was made to 
fit it. 



( yy^ 




CO 



ud 




When the rock was reached, a level bed was cut in its stir- 
face and a ring of masonry built. The water was then pumped 
out of the main tube and the masonry built on the inside. 
As the masonry rose, the partitions, shaft, and the dome were 
removed. When the pier was above the surface of the water, 
the upper part of the cylinder, about fifty feet in length, was 
unboiled and taken awa} T , it having been made in two halves 
for this purpose. 

In this particular case the compressed air was only used in 
the annular chamber, and as this area was small in compari- 
son with the main cylinder, there was no necessity of an extra 
weight to balance its action. 

It is a good example of the pneumatic process combined 
with the principle of the coffer-dam. • 



308 CTVIL ENGINEERING. 

426. Pneumatic caisson. — The next important modifica- 
tion in the pneumatic method was to combine the principle 
of the diving-bell with the common caisson. It is now the 
most commonly used method for situations like that just de- 
scribed in the Saltash bridge, and especially were the founda- 
tions have to support a great pressure. 

It consists essentially of three parts : 1st, The caisson; 
2d, The working chamber ; and 3d, The pneumatic ap- 
paratus and its communications with the working chamber. 

Caisson. — This does not differ in its principles of construc- 
tion from the common caisson already described. The bottom 
is of wood or iron, made strong enough to support the struc- 
ture with its load, and forms the roof of the working chamber. 
The sides are generally of wrought iron, and are not usually 
detached from the bottom when the structure is finished. 

Working chamber. — This is below the caisson, the bottom 
of which forms the roof of the chamber, as just stated. Its 
sides are firmly braced to enable it to resist the pressure from 
th.3 earth and water as it sinks into the ground. The chamber 
is made air and water tight. 

Pneumatic apparatus and communications. — Vertical 
shafts, either of iron or masonry, passing through the roof of 
the chamber furnish the means of communication between 
the working chamber and the top of the caisson. The air- 
locks may be placed in the upper end of the shaft, as in the 
pneumatic pile, or placed at the lower end of the shaft in the 
working chamber. 

The usual supply pipes, air-pumps, discharge pipes, etc., are 
provided as in the other pneumatic methods. 

Sinking the caisson. — It is moored over the place it is to 
occupy and sunk gradually to the bottom as an ordinary cais- 
son. Air is then forced into the working chamber, driving 
out the fluid matter, and the earth and loose material are then 
•dug out, the caisson settling slowly under its own weight and 
that of the masonry until it rests on the firm soil or solid 
irock. 

An outline description of some of those recently used will 
more fully illustrate their construction and the method of 
sinking them. 

427. Pneumatic caisson used at L'Orient, France.— 
This method was used to lay the foundations and build two 
of the piers of a railroad bridge over the river SeorfF, at 
L'Orient, in France. The river bed was a thickness of mud 
from 25 to 45 feet deep, over a hard rock. The mean level 
of the water was about GO feet above the rock, and at high 



PNEUMATIC CAISSONS. 



309 



tide 70 feet. It was essential for the stability of the piers 
that they should rest on the rock. 

The caissons used were 40 feet long, 12 feet wide, and 
made of boiler iron. 

The thickness of the iron forming the sides of the caisson 
varied according to the depth in the water, being greater for 
the lower than for the middle and upper parts. The ratio of 
the thickness was for the upper, middle, and lower, as 3, 4, 
and 5. 

The working chamber was ten feet high and communicated 
with the upper chambers or bells, where the air-locks were 
placed, by two tubes for each bell ; these tubes being each two 
feet and three-quarters in diameter. Each bell was ten feet 
high and eight feet in diameter, and contained two air-locks 
and the necessary hoisting gear; the full buckets ascending 
through one tube and descending through the other. 

Fig. 153 shows the caisson used for the pier on the right 
bank. 



Fig. 153 — Represents a vertical section 
of caisson and masonry of pier during 
the process of sinking. 

A, the working chamber. 

P, interior elevation of caisson. 

C,C, elevation of the bells. 

D,D, the communicating tubes. 

E,E, masonry of pier, built as the caison 
was sinking. 




When the rock was reached, its surface was cleaned off 
and a level bed made under the edges of the caisson. The 
working chamber was then filled up to the roof with ma- 
sonry. 

The pier was of concrete with a -facing of stone masonrv, 
and built up as the caisson was sinking to its place. 

The working chamber being filled, the tubes were with- 
drawn and the spaces occupied by them filled with con- 
crete. 



310 



CIVIL ENGINEERING. 



PNEUMATIC CAISSONS AT ST. LOUIS, MO. 

428. At the time the foundations of the piers of the bridge 
over the Mississippi River, at St. Louis, were laid, the caissons 
that were used were the largest that had ever been employed 
for the purpose. 

This bridge consisted of three spans, supported on two piers 




FlG. 154 — Represents a section of the caisson used in construc- 
tion of east pier of the bridge over the Mississippi 
River, at St. Louis, Mo. 
A, main shaft. B, air-locks. C, working chamber. 
D, sides of caisson. E, side shafts. F, sand pumps. 
G, discharge of sand. 

and the abutments. The river at this point is 2,200 feet wide 
at high water, with a bed of sand over rook. The rook slopes 
from the west to the east, the upper surface of the sand being 
practically level: The depth of the sand on the western shore 
was about 15 feet, and on the eastern nearly 100 feet. 



PNEUMATIC CAISSONS. 311 

As the scour on the bottom is very great in the Mississippi 
River, it was regarded as essential that the piers should rest on 
the rock. To penetrate this sand and lay the foundations on 
the rock, the pneumatic caisson was used. 

Fig. 15 J- represents a section of the one used for the east 
pier. At this point the rock was 128 feet below the high- 
water mark. At the time the caisson was moored in position 
there was a depth of 35 feet of water and 68 feet of sand 
over the rock. 

The caisson was hexagonal in plan, the long sides being 50 
feet each, and the short ones 35 feet each. Its sides were 
made of j)late iron, three-eighths of an inch in thickness, and 
built up as the caisson sank. 

The bottom, which was to support the masonry, was coin- 
posed of iron girders, placed 5^- feet apart. Iron plates, 
•J- inch thick, were riveted to the under side of these girders 
to form the roof of the working chamber. The sides of the 
caisson prolonged below the girders, formed the sides of the 
chamber, and were strongly braced with iron plates and stif- 
fened by angle irons. This chamber, thus formed, was 80 
feet long, 60 feet wide, and had an interior height of ( J feet. 
The interior space was divided into three, nearly equal, parts 
by two heavy timber girders placed at right angles to the iron 
ones, and intended to rest on the sand and assist in supporting 
the roof of the chamber. Openings made through them 
allowed free communication between the divisions. 

Access to the top of the caisson was obtained by vertical 
shafts lined with brick masonry, which passed through the 
roof of the chamber. The air-locks were at the lower end of 
the shafts and within the chamber. 

As the caisson descended, the masonry pier was built 
up in the usual maimer, its foundation being on the iron 
girders. 

Workmen in the chamber excavated the sand, which was 
removed from it by sand pumps placed on the top of the 
caisson. A pump of 3-J- inches diameter was capable, under 
a pressure of 150 pounds on the square inch, of raising 20 
cubic yards of sand 125 feet per hour. 

When the caisson reached the rock, its surface was cleared 
of sand and the entire chamber tilled with concrete. 

The experience acquired in sinking this caisson enabled 
the engineer to make material modifications in the details of 
those subsequently used. 

The health of the workmen was greatly affected by the 
high degree of compression of *the air in which they had to 



312 CIVIL ENGINEERING. 

work, this being as great as fifty pounds on the square inch, 
and several lost their lives in consequence. 

In the second pier, instead of filling the chamber entirely 
with concrete when the rock was reached, he simply closed 
the space around the edges with concrete and then filled the 
chamber with clean sand. 



MO. 

429. This method was used in 1871-2 to lay the founda- 
tions of the piers for a railroad bridge over the Missouri River, 
at St. Joseph, Mo. 

For a similar reason to that given in the last case, it was 
decided to rest the piers on the rock below the bottom of the 
river. The bed rock was about sixty-seven feet below the 
level of high water, and overlaid with mud and sand for a 
depth of from forty to the whole distance of sixty-seven feet, 
depending on the position of the pier. There were six of 
these piers, which were placed in depths of water varying 
from zero to twenty -five feet at the low stage; the difference 
between high and low water being twenty-two feet. Pockets 
of clay, with occasionally a snag and boulders were met with 
in the sand and mud. 

The caisson used for pier No. 4 was made of twelve-inch 
square timber, and was at the bottom fifty-six feet long, and 
twenty-four feet wide. The sides of the working chamber 
were three feet thick, sloping inwards with a batter of Ifi. 
It was built by placing first a row of timbers in a vertical 
position, side by side, for the outside ; then, next to this, a 
row laid horizontally ; and then a third row next to this one, 
in a vertical position as in the first case, for the inside. The 
outer row extended one foot below the middle row, and this 
one a foot below the third. One foot above the bottom of 
the inside row, a horizontal beam extending entirely around 
the interior was bolted to the sides of the chamber. A set of 
inclined struts rested on this piece, and abutted against strain- 
ing beams framed into the roof of the chamber. The roof 
was of timber, laid solid four feet thick, on which rested the 
grillage for the masonry of the pier. The grillage was made 
of timber, seven courses thick, each course being laid at right 
angles to the one below it. The timbers of each course were 
separated by a space of six inches, excepting the top course, 
which was solid. 

All the timber work was accurately fitted, and the whole 



FNEUMATIC CAISSONS. 313 

bolted together so as to form one unyielding mass. The 
interior of the working chamber was calked, and was prac- 
tically air-tight. The dimensions of the chamber were, on 
the inside, twenty-two feet wide and fifty-four long at the 
bottom; live feet wide and seven feet long at the top; and 
nine feet high at the centre. The grillage was drawn in so 
that its top was of the same dimensions as the base of the 
pier, which was nine feet wide and twenty long, with curved 
starlings at each end. 

The air-lock was four feet in diameter and seven high, 
made of plate iron, and placed in the middle of the top of 
the chamber. A door in the top of the air-lock opening 
downwards communicating with an iron vertical shaft three 
feet in diameter, which extended above the top of the ma- 
sonry, allowed access to the top of the caisson. An iron 
ladder in the shaft was used for ascent and descent. The 
usual supply and discharge pipes passed through the grillage 
to the working chamber. 

The caisson was sunk by the process already described. 
The arrangement of the lower bearing surfaces of the cais- 
son are regarded as worthy of notice. The lower edge of 
the outside row of timbers was sharpened, and as soon as it 
had sunk one foot, the under surface of the second or hori- 
zontal row came into play, adding a foot of bearing surface. 
When this had descended a foot, the bottom of the inside or 
third row pressed on the soil, thus giving three feet of bear- 
ing surface. By this arrangement the amount of bearing 
surface was under the control of the engineer. If the soil 
through which the caisson was sinking was variable in its 
nature, that is, on one side of the caisson it was soft, and on 
the other it was hard, the bearing surface could be increased 
on the soft side and diminished on the other. In this way 
the caisson could be kept vertical while sinking. 

The greater part of the material excavated was mud or 
sand, which was discharged easily and rapidly by means of 
sand pumps. The clay, boulders, and snags were discharged 
through the air-lock. 

It was sunk at the rate of from five to seven feet in the 
twenty-four hours. 

The caisson having reached the bed rock, a wall of con- 
crete was built under the edges, six feet wide on the rock, 
and solidly rammed under the three rows of timbers and up 
to and including the horizontal beam supporting the struts. 
Strong vertical posts were placed under the roof to assist in 
supporting it. The sand pumps were then reversed, and the 



314 



CIVIL ENGINEERING. 



chamber filled with clean sand and gravel. A tube was left 
to allow the water in the sand to escape, so that the whole 
interior was compactly filled. The sand pumps were then 
withdrawn, and the shafts filled. 



CAISSONS OF THE EAST RIVER BRIDGE AT NEW YORK. 

430. The caissons used for the foundations of the piers in 
this bridge were rectangular in form, and made of timber. 

The exterior dimensions of the bottom of the chamber in 
the Brooklyn caisson were 168 feet long and 102 wide. 
For the one on the New York side the width was the same, 
but it was four feet longer. 

Both were nine and a half feet high on the inside. The 
roof of the Brooklyn caisson was a solid mass of timber, fif- 
teen feet thick (Fig. 155), and the New York caisson was 
twenty-two feet thick. 




Fig. 155 — Represents section through water shaft of the Brooklyn caisson, 
showing method of removing boulders or other heavy materials. 

The sides of the caisson had a slope of *£ ^ or tne on ^er 
face, and one of \ for the inner, as shown in the figure. The 
outer slope was for the purpose of facilitating its descent 
into the ground. The lower edge was of cast iron, protected 
by boiler iron, which extended up the sides for three feet. 
The sides, where they joined the roof, were nine feet thick. 
The chambers were calked both on the outside and inside, to 
make them air-tight. As a farther security, an unbroken 
sheet of tin extended over the whole roof between the fourth 
and fifth courses, and down the sides to the iron edge. The 
New York chamber was, in addition, lined throughout on the 
inside with a light iron plate, to protect it from fire. 



MOVABLE TNEUMATIC CAISSON. 31.5 

Each chamber was divided into six compartments, from 
twenty-five to thirty feet wide, by five solid timber partitions. 
Communication was had from one to the other by doors cut 
through the partitions. 

The air-locks were placed in the roof, projecting into the 
chamber four feet, and communicating at the top with ver- 
tical shafts of iron, which were built up as the caisson de- 
scended. The locks were eight feet high and six and a half 
feet in diameter. 

The mud and sand were discharged through pipes by the 
compressed air A pipe, three and a half inches in diameter, 
discharged sand from a depth of sixty feet at the rate of one 
cubic yard in two minutes, by the aid of the compressed air 
alone. 

The heavy materials were removed through water shafts. 
These were seven and three-quarter feet in diameter, open at 
the top and the lower end, the latter extending eighteen 
inches below the general level of the excavation. A column 
of water in the shaft prevented the compressed air from 
escaping. 

The material to be removed through the water shaft was 
thrown into the excavation, under its lower end, where it was 
grasped by a " grltpnel bucket,'' which was lowered through 
i he shaft, and then hoisted to the top of the shaft, where it was 
removed. 

The rock being reached,. the chamber was tilled with con- 
crete, in the usual manner. 

The great thick] ess of the roof, and the depth of water, 
enabled the engineer to dispense with the sides of the caisson, 
as the masonry could be kept above the surface of the water 
without its assistance. 



MOVABLE PNEUMATIC CAISSON. 



431. A pneumatic caisson has been successfully used in 
laying the foundations of piers of bridges, which differs from 
those already described, in its construction admitting of its 
being moved after completion of one pier, to another place 
for the same purpose. It is an iron cylinder, ten feet in 
diameter (Fig. 156), connected at its lower end with a work- 
ing chamber, eight feet high and eighteen feet in diameter. 
On the roof of this chamber is an annular chamber, eighteen 
feet in diameter and about six feet high, so arranged as to 
allow of being filled with water when any additional weight 
was necessary, and being emptied of water and its place sup 



316 



CIVIL ENGINEERING. 



plied with compressed air when it was necessary to lighten 
it. On top of this annular chamber was a similar one ar- 
ranged to be loaded with iron ballast. Strong chains attached 
to the roof of the working chamber and connected with a 
hoisting apparatus, placed on a strong scaffolding over the 
site of the pier, were used to lower and lift the cylinder, as 
necessity required. 




Fig. 156 — Represents section of mov- 
able pneumatic caisson. 

B, working- chamber. 

A , chamber for water, or for compressed 
air. 

W, chamber for iron ballast. 

c, c, elevation of lengths of the iron 
cylinder. 



Air-locks, air-pumps, and all the necessary adjuncts of a 
pneumatic pile, were provided and used. Having reached the 
rock or firm soil, the bed and the foundations were con- 
structed as already described. As the masonry of the pier 
rose, the whole apparatus was lifted by the chains and hoist- 
ing apparatus, the cylinder being lightened by expelling the 
water from the chamber, A, and supplying its place by com- 
pressed air. The masonry uf the pier having risen above the 
surface of the water, the whole apparatus was removed and 
used in another place. 

432. Remark. — It is seen that the pneumatic caisson, as 
before stated, is simply a combination of the principle of the 
diving-bell with the common caisson, the diving-bell being on 
a much larger scale, and its roof intended to form a part of 
the bed of the foundation. 

Experience has shown that the large caissons are more 
easily managed than the small ones. The circumstances of 
the case can only decide as to which is preferable, the caisson 
or the pneumatic pile. The method is an expensive one, and 



PROTECTING THE FOUNDATION BED. 317 

is only employed in localities where the others are not ap- 
plicable. 

SECURING THE BED FROM THE INJURIOUS ACTION OF WATER. 

433. The bed of a river composed of sand or gravel is liable 
to change from time to time, by these materials being moved 
by currents in the river. This change, when accompanied by 
an increase of depth, is known as the "scout." Sometimes a 
scour will occur on one side of a structure and not on the 
other, producing in this way, a lateral strain on the masonry. 
Where common piles have been used, they have been known 
to have been washed out by this action. Even in rocky 
bottoms, where they are of loose texture, the rock will grad- 
ually wear away under the action of currents, unless pro- 
tected. 

It therefore becomes an important point to provide se- 
curity for the beds in all soils liable to any change. It is for 
this reason that in very important structures, the foundations 
were placed on the bed rock far below the possible action of 
currents, and so arranged that even if they were exposed to 
them they would be safe. To comply with this requirement 
has caused the free use of the pneumatic methods. 

Various expedients have been used to secure the beds 
where they do not rest on the rock or on a soil below the 
action of the water. A common method is to rip-rap the 
bed, that is, to cover the surface of the bottom, around the 
bed, with fragments of stone too large to be moved by the 
currents, and if the soil is a sand or loose gravel, to use clay 
in connection with them to bond them together. 

Where the bed is made of piles, it is well to enclose the 
piles by a grating of heavy timber before throwing in the 
stone. In some cases the foundations are "boxed, that is, the 
piles are enclosed by a sheeting of planks, or other device, to 
protect them from the scour. 



A. 7 



4 



PART VI. 

CHAPTER XIII. 

BRIDGES. 

434. A bridge is a structure erected over a water-course, 
or above the general surface of the ground, to afford a contin- 
uous roadway between the opposite sides of the stream, or 
above the surface of the country, without obstructing those 
lines of communication lying on the surface beneath. 

A structure of the latter class, or one thrown over a de- 
pression in which there is ordinarily no water, is generally 
-called a viaduct. 

If the structure supports an artificial channel for convey- 
ing water, it is known as an aqueduct, and where this is 
over a stream, it is frequently called an aqueduct-bridge. 

Bridges may, for convenience of description, be classed 
either from the materials of which they are made : as 
masonry or stone, iron, wooden bridges, etc. ; or from the 
character of the structure : as permanent, movable, float- 
ing bridges, etc. ; or from the general mechanical principles 
employed in arranging its parts : as arched, trussed, tubular 
bridges, etc. 

435. Component parts. — A bridge consists of three es- 
sential parts: 

1st, The piers and abutments on which the superstruc- 
ture rests ; 2nd, the frames or other arrargements which 
support the roadway ; and 3d, the roadway, with the parts 
used in connection with it for its preservation or to increase 
its security, as the roof, parapets, etc. 

Bridges are of various kinds, both in their general plan and 
dimensions. These are dependent upon the circumstances 
and the objects requiring the erection of the bridge. 

The simplest bridge is one in which the points of support 



PIERS AND ABUTMENTS. 310 

are so near together that two or more simple beams laid 
across the stream, or opening to be passed over, are sufficient 
for the frame, and a covering of plank laid upon the beams 
forms the roadway. 

The supports being strong enough, the proper dimensions 
to give the beams and the planking are easily determined. 

This calculation is made for the beams under the hypo 
thesis that each is a simple beam, resting on two points of 
support at the extremities, strained by a load uniformly dis- 
tributed over it, and a weight acting at the middle point. 

The uniform load is the weight of the structure, which is 
ordinarily assumed to be uniformly distributed in the direc- 
tion of its length. The weight at the middle represents the 
j^assage of a heavy body over the bridge, as a heavily loaded 
wagon for a common, and a locomotive for a railroad bridge. 
Having determined what this weight shall be, its equivalent 
uniform load may be obtained, and added to that already as- 
sumed, or if preferred, the equivalent weight at the middle 
may be obtained for the uniform load. 

If the number of these beams be represented by n, and we 
suppose that they are at equal distances apart, then the total 
load on the bridge divided b} T n will give the load on each 
beam. Then by formulas already deduced we can, knowing 
the value for B, determine the proper breadth and thickness 
to give each beam. 

436. Platform of roadway.— In a common wooden bridge 
the roadway is generally of planks. These are of hard wood, 
from three to four inches thick, resting on longitudinal 
pieces placed from two to throe feet apart from centre to 
centre. This thickness of plank is greater than is required 
for strength, but has been found necessary to enable the road- 
way to withstand the shocks, friction, and wear due to the 
travel over it. 

If the longitudinal pieces which rest on the supports are 
too far apart to allow the plank to rest directly upon them, 
cross pieces, called roadway bearers, are placed upon them. 
On these cross pieces other longitudinal pieces, called joists, 
are placed close enough together, and upon them the plank- 
ing is laid. 

The particular kind and width of roadway will depend 
upon the character of the travel over the bridge. Knowing 
these, the weight per unit of length is quickly determined. 

437. Piers and abutments.— Walls should be built to 
support the ends of the beams. They may be of stone, wood, 
or iron. Those placed at the ends of the bridge are called 



320 



CIVIL ENGINEERING. 



abutments ; the intermediate ones are termed piers ; the 
distance or space between any two consecutive piers is called 
a span, and sometimes a bay. 

If the frame of the bridge is of a form that exerts a lateral 
thrust, as an arch for instance, the abutments and piers must 
be proportioned to resist this action. 

As their foundations are exposed to the action of currents 
of water,, precaution must be taken to secure them from 
any damage from this source They must also be guarded 
from any shocks from heavy bodies and from the damaging 
effects of floating ice. 

438. Wooden piers and abutments. — "Wooden abut- 
ments may be constructed of crib-work. The crib. is ordinarily 
formed of square timber or logs hewn flat on two of their 
opposite sides. The logs are halved into each other at the 
angles and fastened together by bolts or pins, and further 
strengthened sometimes by diagonal ties. The rectangular 
space thus enclosed is filled with earth or lpose stone. Very 
frequently three sides only of the crib are built. 

Another way of constructing the abutment is to make a 
retaining wall of timber to hold up the earth of the bank. 

The piers are also made sometimes of cribs. The cribs are 
floated to the spot, sunk in place, filled with stone, and built 
up to the proper height. There are serious objections to 
their use for piers, and they are recommended only where no 
injurious results will follow their adoj^tion, and where it is 
not expedient to employ some one of the other kinds. 

The pier made of piles is the most common form of the 
wooden pier. It is constructed by driving piles in a row, 
from three to six feet apart, in the direction of the current. 
The piles are then cut off at the proper distance above the 
surface of the water, and capped with a heavy piece of square 
timber. 

If the piles extend some distance above the water, they 
must be braced by diagonal pieces to stiffen them. 

In some cases the piles are cut off, at or just below the level 
of the water, so that the capping piece will always be kept 
wet. Mortises are made in this cap into which uprights are 
fitted ; the uprights taking the place of the upper parts of the 
piles in the preceding case. Or, what is more common, a 
trestle made in the form of an inverted W is fitted on this 
cap, and the upper side of this capped with a square piece of 
timber. 

Where the bottom is hard and not liable to " wash," the 
piles are dispensed with and the trestle alone is used. In 



FENDERS AND ICE-BREAKERS. 



321 



this case the piece on which the trestle rests is laid flat on the 
bottom and is called the mud-sill. The upper part of the 
trestle is capped as before, and if necessary to get additional 
height another trestle is framed on top of this. 

430. Fenders and ice-breakers. — Wooden piers are not 
constructed to resist heavy shocks from floating bodies. In 
positions where they are to be exposed to this, fenders should 
be built. A clump of piles driven opposite to the pier on the 
exposed side, and some distance from it, will be sufficient to 
protect it, when the current is a gentle one, from ordinary 
floating bodies. The piles should be bound together so as to 
get their combined resistance. This is done by wrapping a 
chain around their heads. If there is danger from floating 
ice, an inclined beam (Fig. 157), protected by iron, should be 
used to break up the ice as it moves towards the pier. 

Elevation. 




Fig. 157. Plan. 



In rapid currents, where the ice is thick, a crib-work in 
plan the form of a square, with one of the angles up-stream, 
has been used. The crib was filled with heavy stone and the 
up-stream augle given a slope and protected by a covering of 
iron. 

The construction in Fig. 158 is a good one. Its resisting 
pow r er is increased by being filled with, stone. 

440. Masonry piers and abutments. — The methods 
described in the chapters on masonry and foundations are 
applicable to the construction of these structures. 

Since they are, from their position, peculiarly liable to 
damage from the action of currents, both on the soil around 
them and upon the materials of which they are made, particu- 
lar attention should be paid to their construction. 
21 



322 



CIVIL ENGINEERING. 



In preparing the bed, if the soil is at all a yielding one, a 
wide footing should be given to the foundation courses, and 
whenever this footing does not rest on rock, means should be 



, 



taken 
water. 



to secure the bed from any injurious action of the 



Elevation. 




Fig. 158. Plan. 



The piers are generally built with a slight batter, although 
they may be built vertical. The thickness given them is 
greater than is necessary to support the load which is to be 
placed upon them, in order that they may better resist the 
shocks from heavy floating bodies and the action of the cur- 
rents to which they are continually exposed. 





Fig. 159. 



-A, horizontal sections of starling-. 
B, same of pier. 



They should be placed, if possible, so that their longest 

current 



dimensions should be parallel to the direction of the 
They should have their up and down-stream faces 



either 



FENDERS AND ICE-BREAKERS. 



323 



curved or pointed, to act as cut-waters to turn the current 
aside, prevent the formation of whirls, and to act as fenders. 

These curved or pointed projections are called starlings. 
Of the different forms of horizontal section which have been 
given them (Fig. 159), the semi-ellipse appears to be the most 
satisfactory. 

Their vertical outline may be either straight or slightly 
curved. They are built at least as high as the highest water 
line, and finished at the top with a coping stone called a 
hood. 

The up-stream starlings, in streams subject to freshets and 
to floating ice, are made with a greater projection than that 
given to the down-stream ones, and are provided with an 
inclined ridge to facilitate the breaking of the ice as it floats 
against them. Where very large masses are swept against 




Fig. 160 — Represents longitudinal section, elevation, and plan of a pier 
of the Potomac aqueduct bridge. 

A, A, up-stream starling, with the inclined ice-breaker D, which rises from 
the low -water level above that of the highest freshets. 

B, down-stream starling. 

E, top of pier. 

F, horizontal projection of ice-breaker. 



the piers, it is not unusual to detach the ice-breakers and 
place them in front of the piers, as in the case of the wooden 
ones. 

Fig. 160 represents the ice-breaker planned and constructed 



324 CIVIL ENGINEERING. 

by Colonel Turnbull, of the Topographical Engineers, United 
States Army, for the piers of the Potomac aqueduct bridge 
of the Alexandria Canal, at Georgetown, D. C. 

The pier was at the bottom 66.6 feet long and 17.3 thick, 
and terminated by starlings whose horizontal cross-section 
was circular. The pier shown in the drawing was 61 feet 
high, and built with a batter of ±2-. 

The starlings were built up with the same batter, except 
that the up-stream one, when at the height of 5 feet below 
the level of high water, received an inclination of 45°, whicli 
it retained until 10 feet above it. From there to the top it 
had the same batter as the rest of the pier. The two lower 
courses of the ice-breaker were 22 inches thick, the rest being 
18 inches. The stones were laid in cement, and no stone*was 
allowed in the ice-breaker of a less volume than 20 cubic 
feet. 

The ice brought down by the river at this point is often 16 
inches thick, and by a current of six miles an hour. On 
these occasions the ice is forced up the ice-breakers to a 
height of 10 or 12 feet above them. The ice breaks by its 
own weight, and passes off between the piers without injury 
to them. 

Probably the ice-breakers of the International Bridge, over 
the Niagara River, at Buffalo, are more severely tested than 
any in our country. They are triangular in plan, with a 
slope of ■§-, and are protected by iron plating. 

441. Iron piers and abutments. — Until a very few years 
ago all piers were made either of masonry or timber. And 
where a solid bed could not be reached by excavation, piles 
were driven, their tops sawed off, and on them a grillage and 
platform was placed to form the bed. 

The substitution of iron for wood in many engineering 
structures, soon caused iron to be used for this class of con- 
structions. 

The form in which iron enters into the construction of piers 
and abutments may be classed as follows : 

1. As piles or columns, wholly of iron ; as screw piles. 

2. As a hollow column, open at the bottom and partly oi 
entirely filled with concrete ; the weight of the bridge resting 
on the iron casing. 

3. As a. cylinder, entirely rilled with masonry or concrete ; 
the weight of the bridge resting on the masonry, the iron 
casing serving as a protection and a means of stiffening the 
column. 

4. As a caisson, when the sides are left standing. 



APPROACHES. 



325 



The precautions recommended for stone and wooden piers 
are equally applicable to those made of iron. 

442. Approaches. — The portions of the roadway, at each 
extremity of the bridge leading to it, are termed the ap- 
proaches. 

These are to be arranged so as to give an easy and safe 
access to the bridge for the vehicles that use it. 

The arrangement will depend upon the locality, upon the 
number and direction of the avenues leading to the bridge, 
upon the width of these avenues and their position, wmether 
above or below the natural surface of the ground. 

When the avenue to the bridge is" in the same line as its 
axis, and the roadway of the avenue and of the bridge is of 
the same width, the abutment is generally made as shown in 
Fig. 161. The returns. or short walls carried back parallel to 




Fig. 161. 



the axis of the road to flank the approach are called wing- 
walls, and are intended to sustain the embankment as well as 
serve as a counterfort to the abutment. 




FiG.162 — Represents a horizontal section of an abutment, A, with curved wing-- 
walls, B, B, connected with a central buttress, C, and a cross tie-wall, D. 



When several avenues meet at the bridge, or it is necessary 
that the width of the approach shall be greater than the road- 



326 



CIVIL ENGINEERING. 



way of the bridge, the wing- walls may be given a curved 
shape, as shown in Fig. 162, in this way widening the 
approach. 

When the soil of the river banks is bad, the foundation of 
the wing-walls should be laid at the same depth as that of the 
abutment. But if the soil is a firm one, they may be built in 
steps, and thus save considerable expense. 

The rules for their dimensions are the same as for other 
retaining walls. A common rule is to make their length one 
and a half times the height of the roadway above the bed of 
the river, their thickness at bottom one-fourth their height, 
and to build them up in off-set on the inside, reducing their 
thickness at top to between 2 and 3 feet. 

In some cases plane-faced wing-walls are arranged to 
have the faces make a given angle with the head of the 
bridge. The top of the wall is given a slope to suit the 
locality, and is covered by a coping of flat stones, which 
shelters the joints and adds a pleasing appearance to the wall 
(Fig. 163). The lower end is generally terminated by a 
newel stone. 




Fig. 163. 



Instead of wing-walls, a single wall in the middle is used 
in many cases. The plan of the abutment in such a case is 
that of a T. 

In this case or in any case, in which there are no wing-walls 
to retain the earth, the abutment wall must be sufficiently 
distant from the crest of the slope of the water-course to 
allow room for the slope of the embankment. This slope of 
the embankment may be the natural slope, or one made 
steeper and revetted with dry stone or sods, as shown in Fig. 
164. 

It may be necessary, to avoid obstructing the conmiunica 



WATER WINGS. 



327 



tions along the bank, to construct arched passage-ways under 
the roadway of the approaches. 




Fig. 164. — Plan and elevation showing a method of arranging the em- 
bankments where there are no wing-walls. 
a, a\ side slopes of embankment of the approach. 
6, b\ dry stone revetment of the slope towards the water-course, 
rf, d\ dry stone facing of the slope of the bank. 
e, e\ paving used on the bottom of stream. 
/, /', stairs for foot passengers. 



443. Water wings. — When the face of the abutment pro- 
jects beyond the bank, an embankment faced with stone should 
connect it with points of the bank, both above and below the 
bridge. These are called water-wings, and serve to contract 
gradually the water-way of the stream at this point. 

Where there is danger of the banks above and below the 
abutment being washed or worn away by the action of the 
current, it is advised to face the slope of the bank with dry 
stone or masonry, as shown in Fig. 164. 

444. The frame. — It is evident that the arrangement used 
to support the roadway admits of the greatest differences in 
form. From these differences in the forms used, many classi- 
fications have been made. 



328 CIVIL ENGINEERING. 

For analysis, they may be classed as follows : 

I. Trussed Bridges ; 

II. Tubular Bridges ; 

III. Arched Bridges; and 
IY. Suspension Bridges. 

Considering the simple bridge to belong to the first class, 
every bridge may be placed under the head of one of these 
divisions, or a combination of them. 



CHAPTER XIY. 

I.— TRUSSED BRIDGES. 



445. A trussed bridge is one in which the frame support- 
ing the roadway is an open-built beam or truss. 

A truss has been defined (Art. 252) to be a frame in which 
two beams either single or solid built, with openings between 
them, are connected by cross and diagonal pieces so that the 
whole arrangement acts as a single beam. 

It is used most generally to sustain a transverse strain aris- 
ing from a weight which it has to support. To do this in the 
best manner, the axes of the pieces of which the truss is com- 
posed are kept in the same vertical plane with the axis of the 
truss or symmetrically disposed with reference to it. 

Supposing the truss to rest on two or more points of sup- 
port, in the same horizontal line, its upper and lower sides 
are called chords. In some cases the upper side has been 
called a straining beam, and the lower a tie. Sometimes 
they are both designated as stringers. English writers call 
them booms. 

Generally, the chords are both straight and parallel to each 
other. They may be and are sometimes both curved, and in 
some cases one curved and the other straight. 

The secondary pieces, or those connecting the chords, are 
called braces, and are so arranged as to divide the frame 
into a series of triangular figures. The braces are known as 
struts or ties, depending upon the kind of strain they have 
to sustain. The triangles may be scalene, isosceles, equila- 
teral, or right angled. They may be placed so as to form a 
system of single triangles, or by overlapping, form a lattice 
or trellis pattern. 



-CALCULATING THE STRAIN ON A TRUSS. 329 

446. Systems. — Trussed bridges are divided into three 
general systems : 

1, The triangular system ; 2, The panel system ; 3, The 
bowstring system. 

Other subdivisions are frequently made, based upon the 
particular arrangement adopted for the braces and the form 
given to the chords. 

Special cases belonging to the systems are generally known 
by the name of the inventor : as Long's truss, Howe's, 
Fink's, etc. 

The essential qualities in a truss are those already given for 
a frame (Art. 231), viz., strength, stillness, lightness, and 
economy of material. 

These qualities are dependent upon the kind of material 
used in its construction, the size of the pieces, and the method 
of arranging them in the frame. The latter gives rise to the 
variety of trusses met with in practice. 



METHODS OP CALCULATING- STRAINS ON THE DIFFERENT PARTS OF 

A TRUSS. 

447. External forces acting on a truss.— It is necessary 
to know all the external forces which act on a truss, to deter- 
mine the strains on its different parts. 

The external forces which are considered, are : 

1, The weight of the bridge ; 

2, The moving or live load ; 

3, The reactions at the points of support ; 

4, The horizontal and twisting forces which tend to 
push the frame in a lateral direction or around some line in 
the direction ef its length. 

1. The weight of the bridge. — Previous to the calcula- 
tion of the strains, the weight is not known, since it -is de- 
pendent upon the thing which we seek, viz., the dimensions 
of the parts of the bridge. An approximate weight is there- 
fore assumed, being taken by comparison with that of some 
similar structure already built. The strains are then 
determined under the supposition that this is the weight 
of the bridge and the dimensions of its parts computed. 
The weight is then calculated from these dimensions, and 
if the assumed weight does not exceed yery greatly that of 
the one computed, the latter is assumed to be the correct 
weight. 



330 CIVIL ENGINEEEING. 

2. The moving load. — This is determined by the objects 
of the bridge, and is taken at its maximum ; that is, as equal 
to or exceeding slightly the greatest load which will ever be 
placed on the structure. This load should be considered as 
occupying various positions on the bridge, and the greatest 
strains in these positions determined. 

For a common road bridge, the maximum load is assumed 
at that which it would be, if the bridge were covered 
completely with men. This load is estimated at 120 pounds 
to the square foot, and must be added to the weight of the 
bridge. 

For a railroad bridge, the maximum load would be when a 
train of locomotives extended from one end of the bridge to 
the other. This load is assumed at one ton (2,240 lbs.) to the 
running foot. 

Sometimes, common road bridges are liable to be crossed 
bj elephants, in which case it is assumed that the strain pro- 
duced is equivalent to that of 7,000 pounds supported on two 
points, six feet apart. 

A load applied suddenly produces on the parts of a bridge 
double the strain which the same load would produce if it 
were applied gradually, beginning at zero and increasing 
gradually until the whole load rested on the bridge. A load 
moving swiftly on the bridge approximates in its effect to 
that of one applied suddenly. 

Therefore, the action of a live load may be considered to 
be the same as that of a weight double that of the live load 
placed carefully on the bridge. This may be treated as an 
additional weight, and added to the weight of the bridge, and 
the strains determined in the usual manner. 

To distinguish these loads, it is usual to call the weight of 
the bridge the permanent or dead load, and that caused 
•by bodies crossing the bridge the moving - , the rolling - , or the 
live load. 

3. "Reactions of the points of support. — The applied 
forces cause reactions at the points of support, which must be 
considered in the calculations, as external forces acting on 
the bridge ; these, therefore, must be determined. No sensi- 
ble error is committed by regarding them as vertical for 
trusses whose chords are straight and are* parallel to each 
other. 

4. Forces producing lateral displacement or twist- 
ing—The action of the wind on the sides of the truss tends 
to push the bridge in a horizontal direction. This pressure 
may be regarded as the action of a uniform load of a given 






KING-POST TRUSS. 331 

number of pounds on tbe square foot of surface against 
which it acts. The best authorities take this force ordinarily 
at forty pounds. The locality will decide as to the amount, 
since the force of the wind is greater in one place than in an- 
other. The gauge has recorded as much as sixty pounds for 
this locality. 

Care is taken to guard against those forces which would 
produce a twisting strain, and their effect reduced to a mini- 
mum. If there be such forces acting, they must be consid- 
ered. 

THE KING-POST TRUSS. 

448. Excepting the triangular frame (Art. 256), the king- 
post truss is the simplest of the trusses belonging to the trian- 
gular system. 

It is frequently employed in bridges of short span, and 
where the span is wide enough to require that the beam 
should be supported at its middle point. 

For a single roadway, two of these frames are placed side 
by side, and far enough apart to allow for the roadway be- 
tween them. Roadway bearers are placed on the beams, or 
suspended from them, to support the joists and flooring. 
Each truss will therefore support its own weight, one- 
half that of the roadway, and one-half of the live load. 
Knowing these weights, the stra'ns on the different parts 
are easily determined, and the dimensions of the parts cal- 
culated. 

To determine the amount and kind of strains on the parts, 
consider the load resting on the beams as uniformly distri- 
buted over them, and represent (Fig. 68), by w, the load on a 
unit of length of the beam, C ; 21, the distance between the 
points of support. 

The load on the beam, C, will be 2wl. The post, g, is so 
framed upon the inclined braces, e, e, and into the beam, C, 
that the middle point of the beam is kept in the same straight 
line with its ends. It is therefore in the condition of a beam 
resting on three points of support in a right line. Five- 
eighths of the load, 2wl, is therefore held up by the king- 
post (Art. 186), and by it transmitted to the apex of the 
frame, producing a tensile strain on the king-post. The 
amount of this strain being known, the dimensions to give 
the king-post are easily calculated. 

The strains upon the braces and their dimensions are de- 
termined as in Art. 256. 






332 



CIVIL ENGINEERING. 




If the middle point of a beam, as A B (Fig. 165), is sup- 
ported at C by inclined braces resting against the abutments, 

the amount and kind of strains 
on the different parts are the 
same as those in the king-post 
truss, excepting that the hori- 
zontal thrust caused by the 
pressure down the braces, in- 
stead of being taken up by 
the beam, will act directly 

If the king-post truss be inverted, 
and supported at the extrem- 
ities (Fig. 166), the amount of 
strain on each piece will be 
the same as before. The 
strains will be reversed in 
kind, that on the beam, and 

that on the king-post, being compression, and those on the 

braces being tension. 



Fig 165. 

against the abutments. 
Inverted king-post. 




Fig 166. 



FINK TRUSS. 

449. Pink truss. — This is the name by which a truss de- 
vised by Mr. Albert Fink, civil engineer, is generally known 
(Fig. 167). It consists of a combination of inverted king-post 
trusses, as shown in the figure. There is a primary truss, 
A B ; two secondary ones, A K C and C L B ; four tertiary 
ones, A P D, D M C, etc. 




M N 
Fig 167. 

The load may be upon the upper or the lower chord, as the 
circumstances may require. The strains on the different 
parts are easily determined, when the weights to be placed 
upon the bridge are known. 

If the load should be on the upper chord, there would be 
no necessity for a lower chord, so far as strength is con- 
cerned. 

450. Bollman truss. — If the braces all pass from the feet 



TRIANGULAR TRUSS. 



333 



of the posts to the ends of the chord, as in Fig. 168, the 
truss thns formed is known as Bollman's trass. 




Fig. 168. 



The calculations for the strains do not differ in principle 
from those made for Fink's truss. It is observed that it dif- 
fers from that truss in having the ties, holding the foot of the 
posts, of unequal length, excepting the set for the middle 
post. 

As in Fink's, there is no necessity for a lower chord if the 
load is on the upper one. 

Both of these constructions are, from the fact that there 
need be but one chord, frequently called "trussed girders," 
to distinguish them from the ordinary bridge-truss, which 
requires two, by the definition given for a truss. 



I. THE TRIANGULAR SYSTEM. 

451. The term, triangular truss, is ordinarily used to desig- 
nate a truss whose chords are connected by inclined braces, 
so arranged as to divide the space between them into isos- 
celes or equilateral triangles, as shown in Fig. 169. 




The braces are generally arranged, in the isosceles bracing, 
so as to make an angle of forty-five degrees with the vertical, 
although sometimes other angles are used. 

When the triangles are equilateral, it is known in England 
and in the United States as the « Warren girder/ 7 and in 
other countries as the " Neville." 

The strains on this truss may be determined by themethods 
given in Arts 260-1-2, or they may be determined by using 
the reactions of the points of support when these are known. 
An example is here given in which the reactions are used. 



334 CIVIL ENGINEERING. 

452. Let it be required to determine the strains upo?i the 
different parts of a triangular truss produced by a weight 
supported at its middle point. 

The truss is supposed to be resting on firm points of sup- 
port at its ends, these supports being in the same horizontal 
line. 

Represent by (Fig. 169), 

2W, the weight resting on the truss at the middle ; 

R, R 2 , the reactions at the points of support ; 

a, the angle R 1 A x S 1 between the brace and a vertical line. 

Since the load is at the middle, the reactions due to it are 
R x == W,andK s = W.. 

If the strain on either half are determined, the remaining 
ones will be known. Take the right half, as shown in the 
figure, and on Rj = W, as a resultant, construct a parallelo- 
gram of forces, the components of which are in the directions 
of the pieces, A 2 B x and A x A 2 . These components will be 

W 

respectively equal to and W tan a. Going to B l5 and re- 
cos a 

W 

solving into two components, one in the direction of 

cos a 

6, B 21 and the other in the direction of B, A 2 , their values 

will be 2W tan a and Performing the same operation 

cos a 
.at A 2 , for the components in the directions of A 2 A 3 and A 2 
B 2 , there are found the same values just determined, 2W tan a 

W 

; and — . At B 2 , A 3 ,s.B 3 , etc., until the point of application 
cos a 

•of the force is reached, similar expressions for the strains will 

be found. 

Hence the strain on B, B 2 is equal to 2W tan a ; on B 2 B 3 , 
this same amount is increased by that on Bj B 2 , or 4W tan a 
for the strain on B 2 B 3 ; on B 3 B 4 , 6W tan a., etc. The strain 
on A, A 2 , is W tan a ; on A 2 A 3 , it is 2W tan a increased by 
that on A, A 2 , or in all, 3\V tan a ; on A 3 A 4 , 5W tan a, etc. 

On the braces there is no increase as we pass from one to 

another, but the same for each, viz., 

cos a' 

An examination of all these strains will show the kind for 
each piece. On the upper chord, the direction of the com- 
ponent of the reaction in the direction of the axis of the 
chord is towards its centre or middle point. The strain is 
therefore one. of compression, and increases from the ends 
until the middle is reached. 



DETERMINING THE STRAIN. 335 

On the lower chord, the strain is in the opposite direction, 
and is therefore a tensile one, increasing in amount towards 
the centre, as already shown. 

On the brace A x B„ and those parallel to it in this half, 
the strain is compressive, and on those not parallel to it, the 
strain is tensile. 

The pieces of the other half are strained equally in amount, 
and are of the same kind, with the exception of a change in 
the kind on the braces ; being tensile in those parallel to the 
brace A x B„ and compressive in the others. 

It will be noticed that these expressions for the strains 
- and for the kind are identical with those already obtained in 
Art. 260. 

The load was taken at the middle point, but if the load had 
been taken at any other point on the truss, the process used 
to obtain the strains would be the same ; it would only be 
necessary to find the corresponding values for R, and E 2 , and 
substitute them in the foregoing expressions. 

453. Let it be required, to determine the strains upon the 
parts of this truss produced by a uniform load distributed 
over the lower chord. 

The effect of the uniform load upon the truss may, without 
material error, be considered to be the same as that produced 
by a series of weights acting at the points A 1? A 2 , A 3 , A 4 , 
etc., each weight being equal to that part of the uniform 
load resting on the adjacent half segments. 

Denote by n the number of these points thus loaded, and 
by 2w, the load at each point. 

Their total weight on the chord will be 2nw, and the 
reactions at the points of support due to them will be, at each 
support, equal to nvj. 

To determine the strains, proceed as before. Construct 
the parallelogram on R^ = nw, and determine the strains on 

72>U) 

Ai Ao and A, Bi, which are found to be nw tan a, and . 

,. . ' cosa 

Going to Bi, the strain on B x B 2 is 2nw tan a, and that on 

o 1WJD 

ft n Ao is . At Ao the components of 2w. acting at this 

j^r* cos a r & 

point in the direction of A 2 A 3 and A 2 B 2 must be subtracted 

from those of the transmitted forces along these lines. The 

strain on A 2 A 3 will therefore be 2nw tan a — 2w tan a == 

2(n — 1) w tan a. To this must be added the strain already 

determined on A x A 2 , which gives the total strain on A 2 A 3 to 

be W[n + 2(n — 1)] tan a. 



336 CIVIL ENGINEERING. 

_. . _ . nw 2lO . . . , 

The strain on A 2 B 2 is , which may be written 

cos a cos a J 

(n — 2)w ^ . ~ , . ^ ~ t -I-.1 

- — ;— ^ — -. Going to B 2 , the strain on B 2 B 3 , produced by the 

COS Qj 

strain on the brace A 2 B 2 , is 2{n — 2)w tan a^ to which the 

strain on Bj B 2 is added, which gives the total strain to be 

2{n — 2) w tan a -\- 2nw tan a, and which may be written 

Mn — l)w tan a. The strain on B 2 A 3 is the same as that on 

. „ (n — 2) w 

A 2 B 2 , or^ '—. 

cos a 

It is plain that the strain on any segment of the npper 
chord is obtained by adding to the strain transmitted to it by 
the brace with which it is connected the respective strains on 
each of the segments preceding it; and that the same law 
obtains for the strains on the lower chord. 

It is to be noticed that the strains on the first pair of braces 
are the same in amount but different in kind, being compres- 
sion on the first and tension on the second, as in the last case, 
and that the amount on the next pair differs from that on the 

2w 

first by ; that the strains on the third pair differs from 

J cos a 7 r 

the second by the same quantity ; and hence, that the strain 

on any pair may be obtained when that on the preceding one 

2w 

is known bv subtracting from it. It is noticed that those 

& cos a 

braces whose tops incline towards the middle point of the 

truss are compressed, while those that incline from it are 

extended. 

It is seen that while the strains on the braces decrease from 
the ends towards the middle, that it is the reverse for the 
chords; in both the upper and lower, the strains increase 
from the ends to the middle. 

The strains thus determined may now be written out, as 
follows : 

1. The compressions on the braces, k x B lf A 2 B 2 , A 3 B s , etc., 
are 

nw (n — 2)w (n — 4) w (n — §)w 

cos a' cos a ' cos a ' cos a ' 

2. The tensions on the braces, Bjt A 2 , B 2 A s , B 3 A 4 , etc., are 
the same in amount, viz., 

nw {n — 2)w (n — 4) >jo 
cos a? cos a ' cos a ' 



DETERMINING THE STRAIN. 337 

3. The compressions on the segments of the upper chord 
are, for B t B 2 , B 2 B 3 , B 3 B 4 , etc., 

2/iw tan a, 4(w — 1) w tan a, 6{n — 2)w tan a, 8(n — 3)w tan a, 

etc. 

4. The tensions on the segments of the lower chord are, for 
Ai A^, A., A3, A 3 A 4 , etc., 

nw tan a, [n + 2 (n — 1)] w tan a, \_n-\-4: (n — 2) w tan <z, 
[n -{- 6 (?i — - 3) ] w tan a, etc. 

General term. — By examining the expressions just ob- 
tained for compression on the segments of the upper chord, 
it is seen that a general term may be formed, from which any 
one of these may be deduced upon making the proper substi- 
tution. Let the segments be numbered from the ends to the 
middle, by the consecutive whole numbers, 1, 2, 3, 4, etc., 
and represent the number of any segment by m. Then, 

2m (n — m + 1) w tan a, 
will be the general term expressing the amount of strain on 
the 7ri th segment. 

It is seen that the term, 

[n + 2 {in — 1) (n — m + lj] w tan a, - 

will represent the amount of tension on the m th segment of 

the lower chord., 

n + 1 
The value of m = — — , corresponds to a maximum for the 

first term, and upon substitution gives j(/i -f Vf w tan a for 
the maximum compression. The value of m — — ~— , corre- 
sponds to a maximum in the second, and upon being substi- 
tituted in it gives •§-[ (n -f l) 9 ' — 1] w tan a for the maximum 
tension. The quantity, n + 1, denotes the number of bays in 
the lower chord, which if we represent by ~N, the expression, 

JN 2 w tan a, 

will very nearly correspond to the maximum tension or com- 
pression upon the chords. 

Strains on the chords. — The strains on the chords do not 
vary constantly but are liniform in each segment. If the 
segments were infinitely short, the strains in that case would 
be a continuous function of the abscissa, and the rate of in- 
crease would be represented by the ordinates of a parabola. 
Suppose a vertical section made at any point, as B 4 , and take 
the middle point of the bay A 4 A 5 , as a centre of moments. 
22 



) 



338 



CIVIL ENGINEERING. 



fcl 



From the principle of moments, there must be for equilib- 
rium, 

d x d = \wv? — R x x y 
or 



C x 



2d 



in which x is the distance of the centre of moments from A x ; 
Cj is the strain on the upper chord at B 4 ; d the distance be- 
tween the axes of the chords ; w the uniform load on the 
unit of length ; and R x the reaction at the point of support A x . 
This is the equation of a parabola wmose axis is vertical and 
whose vertex is over the middle of the bridge. 

Remark. — The usual method of computing the strains 
upon the pieces of a truss is that of adding and subtracting for 
each consecutive piece, as shown in the previous methods for 
calculating strains. General formulas are used in connection 
with these methods to check the accuracy of the computa- 
tions. 



II. THE PANEL SYSTEM. 

454. If the ties of the triangular truss be pushed around 
until they are vertical, this gives the methocl of vertical and 
diagonal bracing referred to in Article 263, and forms the 
type of the truss belonging to this system. In England this 
truss is frequently called the trellis girder, and in France 
the American beam. (Fig. 170.) 



£ 


e B 5 


E 


4 


E 


3 B2 


B, 




''' 


\/ 


\, 






/ 


\/ 




/ 






\ 




/ \ 


\ 






y' >v 










> 


h 


u 


/ 


is 


/- 


u 


4 3 


/ 


\2 


At 



Fig. 170. 



The methods given for the determination of the strains on 
the parts of a Warren truss, and the strains on a frame where 
this method of bracing is used, can be applied to this truss 
and the strains determined. 

The space included between any two consecutive verticals 
is known as a panel, hence the name of the system. 

Diagonal pieces, as shown by the dotted lines in the figure, 



THE QUEEN-POST. 



339 



called counter-braces, are generally inserted in each panel. 
Their particular use will be alluded to in another article. 



THE QUEEN-POST, OR TRAPEZOIDAL TRUSS. 

455. This is the simplest truss belonging to the panel sys- 
tem, and is much used in bridges where the span is not greater 
than forty or fifty feet. Its parts are most strained when 
the load extends entirely from one end to the other. Suppose 
this load to be uniformly distributed over the lower chord, 
A t A 4 , and represent by (Fig. 171), 

Z, the length of the segment A t A 2 ; 

w, the weight on the unit of length ; and by 

<z, the angle of Rj. A t Bf. 




Fig. 171. 



Since the segments A t A 2 , A 2 A 3 , A 3 A 4 , are ordinarily equal 
to each other, 31 will be the length of the lower chord, and 
Swl w T ill be the total load on the truss. The queen-posts are 
framed into the lower chord, so that if it were a single piece 
it would be a case of a beam resting on four points of sup- 
port. Supposing this to be the case, or so connected as to act 
like one piece, each post would sustain -^ of wl. This weight 
is transmitted to the upper end, where it is held in equilib- 
rium by two forces, one acting in the direction of the inclined 
brace, and the other in the direction of the chord B^. The 

01)1 

component in the direction of the brace is equal to \\ 

COS CL, 

and that along the chord, {± wl tan a. The two latter balance 
each other, producing a strain of compression on the piece. 
The other two produce compression on the braces, which is 
transmitted to the points of support, producing a strain of 
tension on the lower chord and a vertical pressure on the 
points of support. Knowing the amount and kind of strains, 
the dimensions of the pieces can be calculated. 

Instead of considering the chord as a beam resting on four 
points of support, it is more usual to consider that one-third 






tb 



fa 






340 CIVIL ENGINEERING. 

of the entire load is held up by each post, and one-sixth at 
each point of support at the ends ; or, if the segments are 
unequal in length, to consider the weight held up by each 
post to have the same proportion to the whole load that the 
segments have to the entire length of the chord A X A 4 . If this 
frame be inverted, the remarks made upon the inverted king- 
post truss will apply to this case. 

The queen-post trass, in its present shape, will not change 
its form under the action of a load uniformly distributed 
over it, and when loaded in this manner, the truss is said to 
be balanced. If, however, the load be only partially dis- 
tributed over it, so that the resultant acts through some other 
point than the middle of the truss, it may become distorted 
by a change of figure in the parallelogram A2BJB2A3. It is 
then said to be unbalanced. 

Sometimes, a certain amount of stiffness existing in the 
joints and of resistance to bending in the pieces, give suffi- 
cient rigidity to the truss, and may be relied upon to prevent 
distortion when the loads are light. 

Generally a change of form will take place as the load 
moves from one point to another, due to the elasticity of the 
materials of which the frame is made and to the imperfection 
of the joints. To prevent this change of form, diagonal 
pieces are inserted, as shown in the dotted lines of the figure. 
The truss is then said to be thoroughly braced. 

A truss is said to be thoroughly braced when the parts are 
so arranged that no distortion takes place under the action 
of the load, whatever may be its position. 

A truss may be distorted and even broken, by an excessive 
load, notwithstanding the use of braces, but this is excluded 
by the definition of a truss, given in Art. 231. 

In the calculations to determine the strains, the material 
of the truss is considered rigid and the joints perfect. 



III. THE BOWSTRING SYSTEM. 

456. The common bowstring girder is one in which the 
upper chord is curved into either a circular or parabolic form 
and has its ends secured to the lower chord, which is straight 
(Fig. 10/). The thrust of the upper beam is received by the 
lower one, which therefore acts as a tie, and as a consequence, 
the reactions at the points of support are vertical. The inter- 
mediate space between the bow and the string is filled with 



BOWSTRING GIRDERS. 



341 



a diagonal bracing, either of the triangular or panel systems, 
for the purpose of stiffening the truss. 

The maximum strains in the chords will be found when 
the truss is uniformly loaded. This load may rest directly 
upon the lower chord or be suspended by vertical ties from 
the upper one. 

Where the span is of considerable length, the usual practice 
is to form the upper chord of a number of straight pieces, 
the intersections of whose axes ar.e in the curve of the bow. 
(Fig. 172.) 











Bs 


B* 








^r*-^"^ / 


/ 


\ 




"f 8 




/ 


/ 


» 


\ 




</\m 




r/''' 


/ 


/ 


\ 
\ 




.. ' 


■--V~^ 


B 2 | 




/ 


/ 


i 


\ 




\ 


f 





A4 



A3 A2 



A, 



Fig. 172. 



To find the strains upon the parts of a truss belonging to 
this system, produced by a uniform load resting on the lower 
chord, which is connected with the upper one by vertical ties 
dividing the truss into an even number of panels of equal 
horizontal length, represent by 

2a, the length of the lower chord ; 
y, the rise of the curve, or depth of the truss at the centre ; 

w, the weight on the unit of length of the lower chord ; 

P 1? the strains on pieces of the upper ; and 

T l5 the strain on the lower chord. 

Take the origin of the co-ordinates at A 1? the axis of X coin- 
ciding with the axis of the lower chord, and Y perpendicu- 
lar to it. 

Disregarding the braces, and supposing the lower chord 
cut in two on the left of A 3 and very near to it, the truss will 
tend to turn about B 3 . 

Taking the moments around this point, their results 



Ti x A 3 B 3 = R^ 



war 



wx , n 



x), (155) 



x, representing the distance AiA 3 . 

Taking the curve containing the intersections B 1? B 2 , B 3 , etc., 
to be a parabola, its general equation when referred to the 
vertex and tangent at that point is 

x 2 = 2py. 



312 CIVIL ENGINEERING. 

The vertex being the origin, the value of y =f gives 
x == ± a, or 

whence, 

a 2 

which being substituted for 2p in the equation of the para- 
bola, gives 

rf = ^y,ory=4<*> • • • ( 156 ) 

Placing the origin at A 1? the equation of the curve will 
be 

CO 

Since A 8 B 3 is equal to y, for the value of x equal to A^, 
there follows from the substitution of this value of A 3 B 3 , in 
equation (155), 

^ _wx (2a - x) _ w a 2 

^-Y—^-^f ' ; (158) 

Hence, the strain on the lower chord, produced by a uni- 
form load, is constant throughout. 

It is observed that this is the same value obtained for the 
horizontal component of the thrust in Art. 228. 

In the same section, taking the moments around A 3 , the 
lever arm of the strain on B 2 B 3 , is A 3 m drawn perpendicular 
to the piece and through the centre of moments. 

There results 

P x x A 3 m = — (2a - x). . . (159) 

2i 

Through B 2 , draw a straight line parallel to the lower 
chord. From the triangles B 2 B 3 ^> and A 3 B 3 m, we have the 
proportion, 

B 2 B 3 : B 2 j) ; ; A 3 B 3 : A 8 m. 

The first term of this proportion is the length of the piece 
of the upper chord for this panel, which represent by v as it 
varies in length for each panel from A t to the centre. The 
second term is the horizontal length of the panel and constant 
which represent by I. Substituting v and I in the proportion, 
we obtain 

v\l\\y\ A 3 m. .-. A 3 m = ?/-, 



BOWSTRING GIRDERS. 343 



or j? i 

A 2 m = —» % (2a — x) — . 

a 2 ; v 

Which substituting in equation (159), we get 

Pi=?f£ m 

This shows that the strain is independent of x and depend- 
ent upon v the only variable present, and that it increases as 
v increases, or is greatest at the points of support. 

Suppose a brace to be inserted in this panel, joining A 2 and 
B 3 , or B 3 and A 3 , and the section taken midway between A 2 
and A 3 . It would cut the upper chord, the lower, and the 
brace. For an equilibrium, the algebraic sum of the hori- 
zontal components and of the vertical components of all the 
forces must be separately equal to zero. 

Represent the straiu on the brace by F, and the angles 
made by the brace and the piece B a B 3 of the upper chord 
with a vertical, by a and j3, respectively. 

The first of these conditions of equilibrium can be ex- 
pressed analytically, as follows : 

P t sin j3 - F sin a — T = 0. 
But P x sin J3 = T = % ~, hence 

F sin a = 0, or F = 0. 

That is, there is no strain on the brace produced by a load 
uniformly distributed over the truss. 

If .the load had been placed directly upon the upper chord, 
there would have been no strain on the verticals. 

If instead of the panel system the triangular had been 
used for the bracing, its use would have been simply to 
transmit the loads on the lower chords to the upper. Know- 
ing the angle made, the strain on any brace could be easily 
determined. 

The vertical component of V t may be obtained as follows : 

Let y' and y" be the ord mates of the lower and upper ex- 
tremities of any piece, as B 2 B s , of the upper chord. 

Denote by v the length of the piece, the intensity of the 
strain on the piece, then y" — y' would represent its vertical 
component. 

From the equation of the curve, we have 

y " ~J 2 x" (2a - x"\ and y' = '\ x' (2a - a?'). 
a a 



344 CIVIL ENGINEERING. 

But x" — x' 4- I, which being substituted in the first of 
these equations for x'' ', and then from this result subtracting 
the second of the equations, we get 

y" -y'= f 4 (2« - 2*' - 1). 

Representing the vertical component by V, we may form 
the following proportion : 

v.y"-y' :: P, : V. 

Substituting for P t and y" — y\ the values just found, and 
solving, we find 

w 
V = 2 Qfa - 2x' - Z), . . (161) 

for the vertical component. 



OTHER FORMS OF BOWSTRING TRUSSES. 

457. The common bowstring girder has been used by 
simply turning it over, so that the lower chord was curved, 
and the upper, straight. There is no difference in principle 
in this case from the one just explained, nor in the amount 
of strains on the different parts. The kind of strains is 
changed, being compression on the straight chord and tension 
on the lower one. 

By combining this inverted one with the other, that is, 
making both the upper and lower chords curved, another 
form is obtained. This arrangment was used by Brunei in 
the Saltash Bridge. 

Where the amount of material forms an important item, 
botli in the weight and cost of the structure, as in the case of 
very large spans, this form can be used to an advantage over 
the other forms of bowstring trusses. 

The great objection to the bowstring truss, compared with 
those of the other systems, is the inferior facilities it affords 
for lateral bracing. 



COMPOUND SYSTEMS. 



458. If two or more of the trusses already described be 
combined, there is formed a class of trusses known as com- 
pound trusses. This term is sometimes limited to a com- 



COMPOUND SYSTEMS. 



345 



bination made of two or more of different systems, partic- 
ular names being given to those made of the same system. 

As they can be always resolved into their simple parts, 
there is no need of a separate classification except for des- 
criptive purposes. 

459. Lattice truss. — If the segments of the simple trian- 
gular bridge truss (Fig. 169) be bisected, and braces inserted 
in the intervals thus formed parallel to the braces already 
used, a truss similar to that shown in the Fig. 173 is formed. 







Fig. 173. 

The dotted lines show the intermediate braces. This is 
called a double triangular truss, although sometimes it is 
known as the half-lattice. 

By dividing the segments into three, four, or more equal 
parts, and inserting a corresponding number of braces, the 
triple, quadruple, etc., triangular trusses are formed. They 
are generally known as lattice trusses, or girders. 

To determine the strains on a truss of this kind, it is usual 
to consider the truss as composed of two, three, four, or more 
simple triangular trusses, as the case may be, and find the 
strains on each one separately. These are then added and 
the strength of the truss considered as that of the whole com- 
bined. Under this supposition, the braces are regarded as 
separate from each other, and only fastened at their ends. 
In fact, they are generally fastened together at their inter- 
sections, which adds to the strength of the combination but 
complicates the problem of finding me amount of strain on 
each piece. 

A subdivision of a truss of the panel system, and putting 
in another set of panels of the same size, will give a compound 
truss which has been much used. A calculation of the 
strains is made in the same way as that j ust described. 



STRAINS PKODtJCED BY A MOVING LOAD. 



460. Loads placed in particular positions, or stationary loads, 
have been the only forces considered in the previous examples. 
As a bridge affords continuous roadway between two points, 



346 CIVIL ENGINEERING. 

it is subjected to strains produced by loads which move over 
it, and it is essential that the action of the moving loads on 
the parts of the bridge be known. 

With the exception of the shearing strain, it has already 
been shown that the strains produced by a moving load are 
the greatest when the centre of the load is at the centre of 
the bridge, and will be at the maximum when the moving 
load covers the entire structure. 

If, then, the maximum moving load that will ever come 
upon the bridge be supposed to have its centre at the middle 
of the bridge, and the parts of the bridge determined under 
this supposition, the bridge will possess the requisite strength. 

When the shearing strain enters as an important element, 
its maximum value should be obtained, and the parts of the 
bridge proportioned accordingly. 

461. Counter-braces. — The dotted lines in Fig. 170 repre- 
sent pieces of the truss known as counter-braces. If the truss 
supports a load at the middle point, or a load uniformly 
distributed over the entire truss, these counter- braces are not 
necessary. In ordinary trusses they are used to resist the 
action of moving loads. 

Take the simple triangular bridge truss, and suppose it 
strained by a live load which is uniformly distributed over 
the lower chord. Let this live load extend from either end 
of the truss and for a distance equal to one-fourth of the span. 
The resultant of the load acts through its middle point, which 
is at a distance from the end of the truss equal to one-eighth 
of the span. 

The nearest abutment, or point of support, will therefore 
support seven-eighths of this live load and the farthest abut- 
ment will support one-eighth. The strains on the chords and 
braces are determined by the methods already explained. 

It is seen that the strains produced by the one-eighth of the 
load going to the farthest point of support are changed in 
kind from the end of the load to the middle of the truss. 
That is, the braces whose tops incline towards the middle of 
the truss are extended by the action of this eighth instead of 
being compressed, and the other braces are compressed by it 
instead of being extended. These particular braces are, with 
the live load in this position, affected by strains from the live 
and permanent loads which are different in kind. The braces 
are therefore, under certain circumstances, liable at onetime 
to be extended and at another time to be compressed, and 
must, whenever this is the case, be constructed to resist both 
kinds of strains. In the panel system, the braces are gener- 



DIMENSIONS OF TRUSS. 347 

ally constructed to take only one kind of strain. In those 
panels where a change of strain is liable to take place, a 
brace must, be inserted to take this new strain. The brace 
inserted for this purpose is called a counter-brace, and has a 
different angle from that given to those used to brace the 
truss under the hypothesis that the strains are produced by a 
load covering the entire bridge, and which are called main 
braces. The main braces are necessary in every panel, and 
it has also been the custom to use counter-braces in every 
panel. It is evident that there is no necessity for counter- 
braces in any of the panels except those between the points 
of "no shearing" strain and the middle of the truss. 



LENGTH AND DEPTH OF A TRUSS. 

462. The length of a truss depends upon the span and 
whether it is to be supported on two or more points of sup- 
port. Assuming that it is to be a single truss resting on two 
points of support, it depends upon the span. The span de- 
pends upon several things : the navigability of the stream, 
character of the freshets, the movement of ice, the practicabi- 
lity of obtaining inexpensive and good foundations, etc. 

Over wide river bottoms, marshes, etc., where good founda- 
tions are easily procured without much expense, the spans 
range from twenty-five to fifty feet. Over important rivers, 
from 150 to 250 feet. 

Extra wide spans are frequently required for bridges over 
very important rivers where they cross the main channel. 
The central span of the Victoria Bridge, over the St. Lawrence 
River, is 330 feet. The channel spans of the Louisville bridge, 
over the Ohio River, are 370 and 400 feet respectively. The 
central span of the St. Louis bridge, over the Mississippi 
River, is 515 feet. 

The depth of the truss, in proportion to its length, varies 
from one-tenth to one-fifteenth in England and from one- 
sixth to one-tenth in the United States. 



THE GRAPHICAL METHOD. 

463. The graphical method is much used to determine 
the strains on the different parts of a bridge truss. This 
method possesses many advantages and grows in favor with 
engineers as it becomes better known. 



348 CIVIL ENGINEERING. 

By its use the engineer is enabled to make an independent 
investigation of the strains and to test the accuracy of his 
calculations by a comparison of the results obtained through 
two independent methods. 

The graphical method is based on the simple principles 
much used in mechanics : that a force may be represented by 
a straight line ; that the force is completely given when 
the length of the line, its direction, and point of applica- 
tion are known ; and that if two forces having a common 
point of application are given, that a third force may be 
determined, which acting at the common point will produce 
the same effect as the two acting simultaneously. This 
third force is determined by the principle of the "parallel- 
ogram of forces." 

464. Two forces having a common point of applica- 
tion. — Suppose two forces, P x and P 2 , acting at the point A 2 
(Fig. 174). 

From any assumed point, as 0, draw a right line parallel 
to the direction of the force P l5 and lay off on this line, ac- 



Fig. 174. 

cording to some assumed scale, the distance M, equal to its 
intensity. From the end, M, of the distance just drawn, draw 
the line M N parallel and equal to P 2 . Join N and by a 
straight line, and N will be parallel and equal to the result- 
ant of Pi and P 2 . Its intensity can be obtained by measuring 
the distance N with the same scale used to lay off M and 
M N. 

If a force equal to and parallel to N acts from A t up- 
wards, there would be an equilibrium among the three forces 
at A t . It therefore follows that if three forces at any point 
are in equilibrium, the three sides of a triangle, which are 
respectively parallel to the directions of these forces, may be 
taken to represent their intensities. 



DETEKMINING THE STRAIN. 349 

Assume any point, as C, and from it draw to the extrem- 
ities and N of N, the right lines C N and C 0. These 
distances, C N and C 0, may be taken as the intensities of 
two components which, acting at A x and parallel to these lines 
may be used to replace the resultant, N. 

And in general, any two right lines drawn from this 
assumed point, which may be called the pole, to the ends of 
the straight line representing a force, may be taken as the 
components of that force. 

465. Any number of forces in the same plane having 
a common point of application. — Whatever be the number 
of forces acting at A 1? the right lines representing their inten- 
sities drawn parallel to their directions and in order, in either 
direction from the right to the left or the reverse, will form a 
polygon whose sides may be taken to represent the forces, 
acting at A t . 

If the last line drawn terminates at the common point of 
application, the forces are in equilibrium ; if not, then the 
right line drawn, joining the extremity of the last side with 
this point, will represent the force, which, being added to 
those acting at A 1? will produce an equilibrium. 

It is evident that if a diagonal be drawn in this polygon, it 
may be taken as the resultant of the forces on either side of 
it and may be used to replace those forces. 

The polygon constructed by drawing these lines parallel to 
the forces is called the u force polygon," and when it ter- 
minates at the point of beginning, the polygon is said to be 
" closed." 

If the forces act in the same straight line, the polygon 
becomes a right line. 

466. A system of forces in the same plane with dif- 
ferent points of application. — It will only be necessary, in 
this case, to produce the lines of direction until they inter- 
sect. It is then the case just considered. It may be that 
the point of intersection will not be found within the limits 
of the drawing. Under this supposition, a point of the re- 
sultant may be determined as follows: 

Let P x and P 2 be any two forces which do not intersect 
within the limits of the drawing, their points of application 
being A t and A 2 respectively. (Fig. 175.) 

Draw M and M N, respectively, parallel to Y t and P 2 . 
The line N will give the direction and intensity of the re- 
sultant of the two forces. From any point, as C, draw the 
right lines^ C and C N. These are the components which 
may be taken to replace N . Assume any point on P l5 as a 



350 CIVIL ENGINEEEING. 

and draw through it the lines, ac and ah parallel to C and 
M C, respectively. Where ah intersects P 2 , as at h, draw ha 
and ho parallel to CM and N C. Produce the lines ac and 
he until they intersect. Their point of intersection will be 
one point of the resultant, which can now be constructed. The 
same method holds good if the forces are parallel. If there 
were more than two forces the same method can be used. 




Fig. 175. 

If perpendiculars are let fall from the point of intersec- 
tion, c, upon the directions of the forces P t and P 2 , it can 
be easily shown that they are to each other inversely as the 
forces. That is, if the perpendicular let fall on P x is repre- 
sented hjp\ and that on P 2 by j/', that there is the following 
proportion : 

This is also true for the perpendiculars let fall from any 
other point of the resultant. 

"'467. Parallel forces. — The principal forces acting on en- 
gineering structures are due to the action of gravity, and in 
these discussions these forces are taken as parallel and vertical. 
Let P l5 P 2 , P 3 , etc., be a system of parallel forces acting at 
L the points A 1? A 2 , A 3 , etc., in the same plane. (Fig. 176.) 

/^ I Lay off from 0, on a straight line parallel to-R, the dis- 

tance 1 equal to its intensity, and from 1 to 2, the inten- 
sity of P 2 , and then from 2 to 3, the intensity of P 8 , etc. The 
straight line of 5 will be the force polygon, and in this 
case equal to the resultant, as all the forces are acting in the 
same direction. From any assumed point, c, as a pole, draw 
straight lines to 0, 1, 2, 3, etc., or extremities of the forces 
just laid off on the line 5. The perpendicular, C H, is 
called the "pole distance." Assume a point on the the right 
of P n as a, and through it draw a straight line parallel to C. 



GRAPHICAL METHOD. 



351 



From the point b, where this line intersects P l5 or P x pro- 
duced, draw a line parallel to C 1, and from the point where 
this intersects P 2 produced, draw one parallel to C 2, etc., 
until lines parallel to all the lines drawn from C have been 
drawn. 

These forces P l5 P 2 , etc., may be supposed to act at these 
points, b, c, d, etc. If the points a and g are h'xed, and the 
others are all connected by flexible cords, the whole arrange- 




Fig. 176. 



ment would form a funicular machine or polygon. The 
three forces acting at any one of these points are represented 
by the three sides of a triangle, and are therefore in equilib- 
rium. The broken line, a, b, c, d, e,f, g, thus formed, is called 
the " equilibrium polygon." 

If ab and gf be produced until they intersect, their inter- 
section will be one point of the resultant of the system of 
forces, and the resultant may at once be constructed. 

4:68. Suppose ag to be the axis of a beam resting in a hori- 
zontal position upon two points of support at a and g, and 
acted upon by a system of forces whose resultants correspond 
in direction with those of the forces P 1? P 2 , P 3 , etc. In order 
that an equilibrium should exist, there must be vertical reac- 
tions acting upwards at these points, a and g, and their sum 
must be equal to the resultant. Represent these reactions by 
E x and Eg- If the resultant passes through the middle point 
of this line, ag, that is, if the forces are distributed symetri- 
cally with respect to the middle point, the reactions will be 
equal to each other. 

Examining the equilibrium polygon, it is seen that the result- 
ant of P x and P 2 must pass through the intersection of ab and 
cd\ that the resultant of 1^ and P 1? through the intersec- 
tion of ag and bo ; of P 1? P 2 , and P 3 , through the intersection 
of ab and de\ and so on. A simple inspection of the force 



352 



CIVIL ENGINEEKINQ. 



polygon will give the direction and intensity of any of these 
resultants. 

469. Bending moment of any section, and the shear- 
ing strain. — Let it be required to determine the bending mo- 
ment and the shearing strain on any section of a beam rest- 
ing on two points of support and holding up four unequal 
weights at unequal distances apart. 

Theorem. — The moment of a force, around any centre 
is equal to the "pole- distance" multiplied by a straight line 
draion through this centre parallel to the force and limited 
by the components of the force. 



Ck. 




h\ 




\_ 


a 




^ 




■h ^^ r*. 


dU<" 


" r ^t' 



Fig. 177. 



Let the force, P (Fig. 177), be resolved into any two com- 
ponents, aCi and aC 2 , which are represented by the right lines 
C 0, C P, drawn from the pole to the ends of the force in the 
force polygon. The moment of P with respect to any point, 
as b, is P x ab. From C 2 draw the line C % p, perpendicular to 
P. This is equal to the " pole distance,'' which represent by H. 
Through b draw,<%£ parallel to P, and limited by C x and C 2 
produced. 
is obtained 



From similar triangles, the following proportion 



P : H : : cd : ab, or Yxab — Ilxcd, 

which was to be proved. 

In Fig. 178 the bending moment at 0' is R x x A 0', which, 
as has just been shown, is equal to H xpp x ; at 0' f the bending 
moment is Kj x AO" — "W^ x A'O". The components of w % 
are ab and be. Hence the moment of W t at 0"is II xp\p,,, 
and the total moment is II xp'p\. 

And as this is true for any section, it is seen that the bend- 
ing moments are proportional to the ordinatcs drawn from 
the dosing line to the sides of the equilibrium polygon. And 
at any section, it is equal to the product of II and the ordin- 



GRAPHICAL METHOD. 



353 



ate of the equilibrium polygon corresponding to the section 
under consideration. 




Fig. 178. 

The ordinate is measured by the scale used for the equilib- 
rium polygon, and the pole distance, H, by the scale for the 
^orce polygon. These may be drawn on the same or different 
scales, whichever is the most convenient. 

Representation of the shearing strain. — The shearing 
force between R t and W^ is E 1 . At W u the shearing force is 
Rx— Wj ; at W 2 , it is ¥L l —W 1 —W 2 , etc. Hence, the line, 1^, 1, 
2, 3, etc., represents graphically the shearing forces for all 
parts of the beam. 

An examination of the figure shows that the shearing force 
is greatest where the bending moment is the least, and the 
reverse. 

470. Couples. — It has been assumed, in the previous dis- 
cussions and examples, that the forces were in equilibrium, 
or by the addition of a single force an equilibrium could be 
established. 




Fig. 179. 



If two forces form a couple, they cannot be replaced by a 
single force. Let F t and P 2 be a couple (Fig. 179), and 12 
the force polygon. 
23 












354 



CIYIL ENGINEERING. 







It is seen that this force polygon closes, that is, the result- 
ant is zero. From any point on P t draw ac and ah parallel to 
C and 1 C. At b, where ah intersects P 2 or P 2 produced, 
draw lines parallel to C 1 and 2 C. The lines ac and bd are par- 
allel. Therefore the equilibrium polygon will not close, or the 
lines will intersect at an infinite distance. A result which 
was to be expected. (Art. 98, Analytical Mechanics.) 

The figure shows that the components of the forces P a and 
P 2 , which act in the direction of the line ah, are equal and 
directly opposed to each other, and that the other two are 
parallel, forming a couple. Hence, it is concluded that a 
couple can be replaced by another without changing the ac- 
tion of the forces. 

From what has been shown, it is evident that if both the 
force and equilibrium polygon close, that an equilibrium exists 
among the forces. But if the force polygon closes and the 
equilibrium does not, that the forces cannot be replaced by a 
single force, but only by a couple. 

471. Influence of a couple. — Let A B (Fig. 180) be abeam 
supported at its ends and acted upon by the couple Y x P 2 . « 




Fig. 180. 

Construct the force polygon, 12, and from a pole, C, 
draw the lines C 0, C 1, and C 2 to the ends of the forces on the 
polygon. From an assumed point, A, on a perpendicular 
through A, draw ah parallel to C. Through its intersection 
with r t produced, draw he parallel to 1 C, and from its 
intersection with P 2 , draw cd, parallel to 2 C. Join a and d, 
and this will be the closing line of the polygon. Parallel to 
this line draw Cg in the force polygon. An examination of 
the force polygon shows that £ g is the vertical reaction act- 
ing upwards at A, which, with the component Cg, may be 
used to replace the force C or ah. 

The ordinates drawn from the closing line, ad, upon the 
sides, ah, be, and ad, represent the law of change in the mo- 
ments. 



GRAPHICAL METIIOD. 



355 



In the preceding examples the force polygon has been given, 
and from it the equilibrium polygon has been constructed. 
Inversely, the equilibrium polygon being given, the force 
polygon is easily constructed. 

472. From the preceding demonstrations, the following 
theorem may be enunciated : 

Theorem. — If straight lines be drawn through any as- 
sumed point' parallel to the sides of a polygonal frame, then 
the sides of any polygon whose angles lie on these radiating 
lines may be taken to represent a system of forces which, if 
applied to the angular points of the frame, will be in' equi- 
librium among themselves. And the converse, that if a sys- 
tem of external forces acting at the angles of a frame are in 
equilibrium, that drawing from an assumed point' straight 
lines parallel to the sides of the frame, and then drawing 
straight lines parallel to the directions of these forces whose 
successive intersections are on the successive radial lines, the 
distances cut off by the second set will represent the strains 
on the corresponding sides of the frame. 

Let ABC (Fig. 181) be a triangular frame acted upon at 
the points A B C by a system of external forces which are in 
equilibrium. Let P t P 2 P 3 be the resultants of the forces act- 
ing at these points, and suppose that these resultants are in 
the plane ABC. 

From an assumed point, P, draw the straight lines, P 1, P 2, 






i 


4 


p 'fy 


/ 


^X 


cl/ 




^^A 




Pr 


1 



Fig. 181. 

and P 3, respectively, parallel to the sides A B, B C, and C A. 
Through an assumed point, as 0, on the line P 3, draw the line 
M parallel to the direction of the force P 1? and from its point 
of intersection with P 1, draw the line 1 2 parallel to the force 

Join N and by a straight line, and this will be parallel to 
the force P 3 . The triangle, M N, will be the force polygon. 

The distance, P 0, will measure the force acting along the 
piece AC; P M, that along A B ; and P N, that along B C. 



356 CIVIL ENGINEERING. 

If the external forces are parallel the polygon becomes a 
straight line, which will be divided into segments by the lines 
drawn parallel to the sides of the frame. Each segment will 
represent the external force acting at one of the angles of 
the frame, and the distances cut off will represent the forces 
acting along the adjacent pieces. 

An application of these principles Avill enable the student 
to determine graphically the strains on the different parts of 
a frame, and test the accuracy of calculations already made 
by other methods. 

WORKING, PROOF, AND BREAKING LOADS. 

473. Ultimate strength of a structure. — The object of 
the calculations made to determine the strength of a given 
structure is to find the load which, placed on the structure, 
will cause it to give way or break in some particular way. 
This load is called the ultimate strength or breaking load 
of the structure. 

Working load. — As the bridge must not be liable to yield 
or give way under any load which it is expected to carry, 
it is made several times stronger than is actually necessary to 
sustain the greatest load which it will ever have to support. 
The greatest load thus assumed is called the "working load. 

The ratio of the breaking load to the working load, or 
"factor of safety," is assumed arbitrarily, limited by experi- 
ence. It is usually taken from four to six for iron, and even 
as high as ten for wooden bridges. It should be large enough 
to ensure safety against all contingencies, as swift rolling 
loads, imperfect materials, and poor workmanship. 

Proof load. — Wiien the bridge is completed, it is usual to 
test the structure by placing on it a load greater than it will 
ever have to support in practice. A train of locomotives for 
a railroad bridge, and a crowd of men, closely packed, upon 
an ordinary road bridge, are examples. These loads are 
known as proof loads. 

A proof load should remain on the bridge but for a short 
time, and should be removed carefully, avoiding all shocks. 
Excessive proof loads do harm by injuring the resisting pro- 
perties of the materials of wmich the bridge is built. 



WOODEN BRIDGE-TRUSSES. 

474. Both the king and queen-post trusses, as stated in a 



LATTICE TRUSS. 



357 



previous article, are frequently made entirely of wood, and 
used in bridges of short spans. 

A compound truss, entirely of wood, the outline of which 
is shown in Fig. 182, has been used in bridges for spans of 
considerable width. 




Fig. 182. 



The celebrated bridge at Schaffhausen, which consisted of 
two spans, the widest being 193 feet, was built upon this 
principle. 

475. Town's lattice truss. — This truss was made entirely 
of wood, and at one time was much used in bridge construc- 
tion. It belongs to the triangular system. The chords (Fig. 
183) were built of beams of timber, and frequently of plank of 
the same dimensions as that used for the lattice. They were 
in pairs, embracing the diagonals connecting the upper and 
lower chords. The diagonals were of plank, of a uniform 
thickness and width, equally inclined towards the vertical and 
placed at equal distances apart. They were fastened to the 
chords, and to each other at their intersections, by treenails, 
as shown in the figure. 




Z73Z*3: 



Fig. 183. 



This truss was frequently made double. In which case 
the lattices were separated by a middle beam, as shown in 



358 



CIVIL ENGINEERING. 



the cross-section in Fig. 183. The chords, instead of being in 
pairs, were made of three beams, placed side by side. 

When the truss was of considerable depth, intermediate 
longitudinal beams were used to stiffen the combination, as 
shown in the figure. 

This truss possessed the advantages of a simple arrange- 
ment of its parts and ease of construction. It also possessed 
the disadvantages of a waste of material and the fault of con- 
struction by which the strength of the truss depended upon 
the strength and the perfect fitting of the treenails. 



m K 



m 



<4 




Fig. 184 — Represents a panel of Long's truss. 
A and B, upper and lower chords. 

C, C, uprights, in pairs 

D, main braces, in pairs. 

E, counter-brace, single. 

a, a, mortises where gibs and keys are inserted. 

b, b, blocks behind uprights, fastened to the chord. 

F, gib and key of hard wood. 

476. Long's truss. — This trass belongs to the panel sys- 
tem, and was built entirely of wood. It was one of the earlier 
trusses used in the United States, and takes its name from 



359 

Colonel Long, of the Corps of Engineers, United States 
Army, who invented it. It was one of the first trusses in 
which a scientific arrangement of the parts was observed. 
(Fig. 184.) 

All the timber used in its construction had the same dimen- 
sions in cross-section. 

Each chord was composed of three solid-built beams, placed 
side by side, with sufficient intervals between them to allow of 
the insertion of the uprights. The uprights which connected 
the chords were in pairs, and fastened to the chords by gibs 
and keys. These gibs were inserted in rectangular holes made 
in the chords, and fitted in shallow notches cut in the up- 
rights. Pieces of wood wide enough to fill the space between 
the beams, about three or four inches thick and two feet long, 
were inserted between the beams of the chords, behind the 
uprights, and fastened to the beams by treenails. These were 
for the purpose of strengthening the uprights and preventing 
their yielding at the notches. 

The main braces were in pairs, and were joined to the up- 
rights, as shown in the figure. The counter-braces were single, 
and were placed between the main braces, abutting against 
or fastened upon the upper surface of the middle beam of 
the chords. Generally they were fastened to the main braces 
by treenails at their intersections. 




Fig. 185. 



477. Burr's tiuss. — This is another of the earlier wooden 
trusses, much used at one time in the United States. This 
truss (Fig. 185) belongs to a compound system, being com- 
posed of a truss of the panel system, stiffened by solid-built 



360 



CIVIL ENGINEERING. 



curved beams, called arch timbers. These arch timbers 
were in pairs, embracing the truss and fastened to it at the 
different intersections of the pieces of the truss with the 
curved beams, as shown in the figure. 

478. Other forms of wooden trusses. — Those trusses 
already named may be considered as the typical ones. There 
are many others, all of which may be referred to one of the 
systems already given, or a combination of those systems. 
Haupt's lattice, Hall's lattice, McCallum's truss, etc., are 
examples of some of the different forms of wooden bridge- 
trusses. 



BRIDGE-TRUSSES OF WOOD AND IRON. 

479. Canal bridge. — A truss composed of wood and iron, 
which has been much used for common road bridges over the 
New York State canals, is shown in Fig. 186. 




Fig. 186. 



In this truss, the chords and diagonals are of wood, and 
the verticals of iron. In some cases, the lower chord is also 
of iron. 

480. Howe's truss. — A popular truss for bridges, both 
common and railroad, and which has probably been used 
more than any other single one, is known as the Howe truss. 
(Fig. 187.) 

This truss belongs to the panel system. The chords and 
braces are made of wood, and the verticals of iron. 

The chords are solid-built beams of uniform cross-section 
throughout. 

The braces are also of uniform size, the main braces being 
in pairs, and the counter-braces single, and placed between 
the main braces, as in Long's truss. Between the ends of 



nOWE S AND PRATT S TRUSSES. 



361 



the braces and the chords, blocks of hard wood or of cast iron, 
inserted in shallow notches in the chords, are used as shown 
in the figure. The faces of the blocks should be at 



angles to the axes of the braces. 



right 




Fig. 187. 



The verticals are in pairs, and pass through the blocks and 
chords, and are secured by nuts and screws at both ends, or 
with heads at the ends with a nut and screw arrangement at 
the middle. By tightening the screws, the chords are drawn 
towards e£ch other, and the reverse. To prevent the edges 
of the nuts from pressing in and injuring the timber, washers, 
or iron plates, are placed between the nut and the wood. 

Where the pressure on the block is great, an iron block or 
other arrangement is placed between the block on one side 
and the washer on the other, to prevent the block from 
crushing into the chord. 

It is seen that there is an excess of material used for the 
chords and the braces. The corresponding gain obtained in 
reducing the amount of material, by proportioning them to 
the strains they would have to support, would not pay the 
cost of extra time and labor required to do it ; they are there- 
fore made, as a rule, with a uniform cross-section. 

There would be a gain if the verticals were proportioned 
to the strains which they have to support, instead of having 
them of uniform size. 

It is observed that the framing is such that the diagonals 
will only take a compressive strain, and the verticals a tensile 
one. 

481. Pratt's truss. — If the framing of the Howe truss 
is changed so that the diagonals will only take a tensile strain, 
and the verticals a compressive one, there results the truss 



362 CIVIL ENGINEERING. 

known as Pratt's. The chords and verticals in this case are 
of wood, and the diagonals are of iron. 

482. There are quite a number of trusses besides those 
just named, which are composed of wood and iron. Those 
mentioned are typical ones, and illustrate fully the method 
of combining the two materials in the same structure. 



IRON BRIDGE-TRUSSES. 

483. Bridge-trusses made entirely of iron are now much 
used. They are made of wrought iron throughout, or of cast 
and wrought iron in combination. Opinions are divided 
among bridge builders as to which should be preferred. In 
the United States a combination of the two kinds of iron is 
more generally used. 

The trusses made of iron belong to all three of the systems 
before named : the triangular, the panel, and the bowstring 
systems. In the combination, cast iron is used for the mem- 
bers subjected to compression; and wrought iron for those 
subjected to tension. Fink's, Bollman's, Warren's, Jones's, 
Whipple's, Murphy- Whipple, Linville, Post's, etc., are some 
of the trusses made entirely of iron which are most frequently 
seen in use in the United States. 

Fink's truss. — The principles of Fink's truss are given in 
Art. 449. The arrangement of its parts enables the truss to 
resist in the best manner the effect produced by a moving 
load, or by changes of temperature. The lower extremities 
of the verticals being free to move, the verticals remain 
normal to the curve assumed by the chord under the strain- 
ing force, and the distances of their lower ends from the con- 
nection of the ties with the chord remain relativel} 7 the 
same. ^None of its parts are therefore unequally strained by 
the force producing the deflection. 

Bollman's truss. — The principle on which this truss is 
constructed is mentioned in Art. 450. In order to avoid the 
ill effects of unequal expansion or contraction of the ties pro- 
duced by changes of temperature, a compensating link is 
used, by means of which the pin holding the ties is enabled 
to change its position as the ties contract or expand, without 
straining the verticals. 

Warren's truss. — The principle of this truss is explained 
in Article 451. It is ordinarily made entirely of wrought 
iron. In some cases the braces are of cast iron, in the form 
of hollow pillars, with wroiight-iron ties enclosed. The brace 



363 



is thus composed of two distinct parts, and is better suited to 
resist the strains which it has to sustain. 

Jones's truss. — This truss is the Howe truss in principle, 
all the parts being of iron. 

Whipple's truss. — This truss is one of the first used 
in this country made entirely of iron. It is composed of 
cast and wrought iron ; the former being used for the 
compression members, and the latter for the tension mem- 
bers. 

This truss (Fig. 188) belongs to the panel system. The 
upper chord is usually made of hollow tubes of cast iron, in 
sections, whose lengths are each equal to a panel distance. 




Fig. 188. 



The lower chord is made of links, or eye-bars, of wrought 
iron, which fit upon cast-iron blocks. These blocks hold the 
lower ends of the vertical pieces. 

The vertical pieces are of cast iron, and are so made that 
the inclined pieces can pass through the middle of them. 
The parts are frequently trussed by iron rods, to prevent 
bending. 

The inclined pieces are wrought-iron rods, and it is seen 
that each of them, excepting those at the ends, crosses two 
panels. 

An examination of this truss shows that the inventor has 
considered economy of material in making the verticals, 
struts, and the diagonals, ties. In principle it corresponds 
with the Pratt truss. 

Murphy- Whipple truss. — This is the Pratt truss, entirely 
of iron, with some of the details of Whipple's. 

jLinville truss. — This is Whipple's truss made entirely 
of wrought iron, the verticals being wrought-iron tubular 
columns. 

Post's truss. — This truss is composed of cast and wrought 
iron. Its peculiarity lies principally in its form (Fig. 189) ; 



364 



CIVIL ENGINEERING. 



the struts, instead of being vertical, are inclined towards the 
centre of the bridge, making an angle of about 23° 30' with 
the vertical, as shown in the figure. The ties cross two panels, 
and make an angle of 45° with the vertical. The counter- 
ties make the same angle, but cross only one panel. 




Fig. 189. 



The inclination given to the struts was for the purpose of 
obtaining the same strength with a less amount of material 
than that obtained when the struts were vertical. 

Lattice trusses. — Lattice trusses, made entirely of iron, 
are frequently used in railroad bridges. They do not differ 
in principle from the lattice truss made of wood. 



CONTINUITY OF THE TRUSS. 



1* 



484. Various opinions have been held as to the advantages 
obtained in connecting the trusses over adjacent spans, so 
that the whole arrangement should act as a single beam. 

If the load is permanent, or the weight of the structure 
is very great, compared with the moving load, it is advisable 
to connect the trusses, so that they shall act as a single con- 
tinuous beam. 

But when this is not the case, the effect of a heavy load is 
to reverse the strains on certain members of the trusses over 
the adjacent spans ; a result which is to be avoided, and hence 
the trusses are ordinarily not rigidly connected. 



WROUGHT-IRON BRIDGES. 365 



CHAPTER XV. 

II— TUBULAR AND IRON PLATE BRIDGES. 

485. Bridges of this class are made entirely of wrought 
iron. 

A tubular girder is one which is made of iron plates, 
riveted together so as to form a hollow beam. These girders 
may be placed side by side and a roadway built upon them, 
forming a simple bridge, which in principle, would not differ 
from the simple bridge described in Art. 435. 

When the tube is made large enough to allow the roadway 
to pass through it, it is called a tubular bridge. 

The difference in construction between the tubular bridges 
and the tubular girders consists in the arrangements made to 
stiffen the four sides of the tube. 

The three great examples of tubular bridges are the Bri- 
tannia Bridge, across the Menai Straits, in Wales ; the Conway 
Bridge, over the Conway River, in Wales ; and the Victoria 
Bridge, over the St. Lawrence River, at Montreal, Canada. 

The Britannia Bridge consists of two continuous girders, 
each 1,487 feet long, resting on three piers and two abut- 
ments. Each tube is fixed to the central pier and is free to> 
move on rollers placed on the other piers and abutments., 
The middle spans are 459 feet each, and the shore spans are 
230 feet each. The bridge is 100 feet above the surface of 
the water. 

The Conway Bridge consists of two tubes, separated by a 
few feet, over a span of 400 feet. 

The Victoria Bridge is a single tube, 6,538 feet long, rest- 
ing on piers, forming twenty-four spans of 242 feet each, and 
a centre span of 330 feet, or twenty-five spans in all. The 
tube is made continuous over each set of two openings, the 
middle of the tube being fixed at the centre pier of the open- 
ing and the extremities free to move on rollers placed on the 
adjacent piers. 

The centre span is level, and is about sixty feet above the 
surface of the water. From the centre span the bridge slopes 
downward at an inclination of j^j. 



366 



CIVIL ENGINEERING. 



In the Conway and Britannia bridges, the tops and bottoms 
are made cellular ; that is, the plates are so arranged as to 
form rows of rectangular cells (Fig. 190). The joints of the 
cells are connected and stiffened by covering plates on the 
outside and by angle-irons within. 



Jl 



i 



~ir 



jL 



d d 


d 


d , 


Tl 




/h 




e: 


i 


f 

* 






B 










* 




P| 


_J 


d ! 



Fig. 190. 



Fig. 191. 



The top, A, is composed of eight cells, each of which is one 
foot and nine inches wide, and one foot and nine inches high, 
interior dimensions The bottom, C, is divided into six cells, 
each of which is two feet and four inches in width, and one 
foot and nine inches high. These dimensions are sufficiently 
large to admit a man for painting the interior of the cells and 
for repairs. 

The sides, B, are composed of plates set up on end (Fig. 
192), their edges adjoining, and connected by means of verti- 
cal T-iron ribs, f it f (Fig. 190). The horizontal joints of the 
side plates are fastened by covering strips. The connection 
between the sides and top and bottom is strengthened by 
gussets, A, A, riveted to the interior T-irons. 



WKOUGHT-IRON BRIDGES. 



367 



Fig. 192. 



In the Victoria Bridge the top and bottom, instead of being 
cellular, consist of layers of plates riveted together and stif- 
fened by means of ribs (Fig. 191). The 
top. A, is slightly arched, and is stiffened 
by longitudinal T-irons, d, d, d, placed 
abont two feet three inches apart, and by 
transverse ribs, <?, about seven feet apart. 
The bottom, c, is stiffened by T-shaped 
beams, g, which form the cross-pieces of 
the roadway. 

Erectioa of tubular bridges. — There 
are three methods which have been used 
to place the tube in position : 1, building 
the tube on the ground, and then lifting 
it into place ; 2, constructing the tube, 
and moving it endwise upon rollers, on 
the piers ; and 3, building it in position on a scaffold. 

The first of these methods was adopted for the Britannia 
Bridge and the third for the Victoria Bridge. 

Cambering-. — If the top and bottom of the tube were made 
horizontal, the tube would when placed in position suffer 
deflection at the middle point from its own weight. In order 
that it may be horizontal after it has fully settled in position, 
the tube is made convex upwards. This convexity is called 
the camber of the tube or truss. The equation for maximum 
deflection of a beam in a horizontal position resting upon two 
points of support will give the amount of camber to give the 
tube. The camber given the Britannia Bridge was eighteen 
inches. 

Remark. — Tubular bridges of these types are not now in 
much favor with the engineering profession, and few, if any, 
will ever be built in the future. The same amount of mate- 
rial in the form of a truss bridge will give a 
better bridge. 

4$6. Plate bridges. — If we were to sup- 
pose the top removed from the tubular bridge, 
or to suppose the diagonals of the lattice truss 
to be multiplied until the side was a con- 
tinuous piece, we would obtain the plate 
girder. In cross-section, the girder is x-form 
(Fig. 193). Its general construction conforms 
to that given for the tubular bridge. 

The joints of the nanges, A and B, are con- 
nected by covering plates; the web, C, is gen- 
erally of thin plate. The web and flanges are fastened by 



w 




/v 



A 



368 ctvtl engineeeikg. 

angle-irons, D, riveted to both of them. The sides are stif- 
fened by T-irons, as in the tubular bridges. 

The advantages gained by using this class of bridges are 
confined to shallow bridges of moderate span. When the 
span exceeds sixty feet, it is more economical to use one 
of the iron trusses already named. 



CHAPTEE XYI. 

in.— ARCHED BRIDGES. 

487. Arched "bridges are made either of masonry, of iron, 
or of steel. 

The form of arch most generally used is the cylindrical. 
The form of soffit will be governed by the width of the 
span, the highest water level during the freshets, the ap- 
proaches to the bridge, and the architectural effect which 
may be produced by the structure, as it is more or less ex- 
posed to view at the intermediate stages between high and 
low water. 

Oval and segment arches are mostly preferred to the full 
centre arch, particularly for medium and wide bays, for the 
reasons that for the same level of roadway they afford a 
more ample water-way under them, and their heads and 
spandrels offer a smaller surface to the pressure of the water 
during freshets than the full centre arch under like circum- 
stances. 

The full centre arch, from the simplicity of its construc- 
tion and its strength, is to be preferred to any other arch for 
bridges over water-courses of a uniformly moderate current, 
and which are not subjected to considerable changes in their 
water-levels, particularly when its adoption does not demand 
expensive embankments for the approaches. 

If the spans are to be of the same width, the curves of the 
arches should be the same throughout. If the spans are to 
be of unequal width, the widest should occupy the centre of 
the structure, and those on each side of the centre should 
either be of equal width, or else decrease uniformly from the 
centre to each extremity of the bridge. In this case the 
curves of the arches should be similar, and have their spring- 
ing lines on the same level throughout the bridge. 



ARCHED BRIDGES. 369 

The level of the springing lines will depend upon the rise 
of die arches, and the height of their crowns above the water- 
level of the highest freshets. The crown of the arches should 
not, as a general rule, be less than three feet above the high- 
est known water-level, in order that a passage-way may be 
left for floating bodies descending during freshets. Between 
this, the lowest position of the crown, and any other, the rise 
should be so chosen that the approaches, on the one hand, 
may not 'be unnecessarily raised, nor, on the othe other, the 
springing lines be placed so low as to mar the architectural 
effect of the structure during the ordinary stages of the water. 

±8S. Masonry arches. — These may be of stone, of brick, 
or of mixed masonry. The methods of construction, already 
described under the heads of Foundations and Masonry, are 
applicable to the construction of masonry arches used for 
bridges. As the foundations and beds of the piers and abut- 
ments are exposed to the action of the water, precaution 
should be taken to secure them. (Art. 440.) 

Centres. — The centres used should be strong, so as to settle 
as little as possible during the construction of the arch, and 
for wide s])ans, should be so constructed that they can be 
removed without causing extra strains on the arch. This is 
effected by removing the centering from the entire arch at 
the same time. Removing the centering is termed striking 
the centre. 

In wide spans, the centres are struck by means of an 
arrangement of wedge blocks, termed striking plates. This 
arrangement consists in forming steps upon the upper surface 
of the beam which forms the framed support for the centre. 
On this a wedge-shaped block is placed, on which rests an- 
other beam, having its under surface also arranged with steps. 
The struts of the rib of the centering either abut against the 
upper surface of the top beam, or else are inserted into cast- 
iron sockets, termed shoe-plates, fastened to this surface. 
The centre is struck by driving back the wedge block. When 
the struts rest upon intermediate supports between the abut- 
ments, folding wedges may be placed under the struts, or else 
upon the back pieces of the ribs under each bolster. The 
latter arrangement presents the advantage of allowing any 
part of the centre to be eased from the soffit, instead of de- 
taching the whole at once, as in the other methods of striking 
wedges. 

Another method of striking centres is by the use of sand. 
In this method, the centres rest upon cylinders filled with sand. 
These cylinders are arranged so that the sand can run out 
2± 



370 



CIVIL ENGINEERING. 



slowly near the bottom. When ready to strike the centre, 
the sand is allowed to ran out of the cylinders, and all the ribs 
gradually and evenly settle down away from the soffit. The 
sand having run out, the centre can then be removed in the 
ordinary manner. 

489. Iron arched "bridges. — Next to masonry, cast iron is 
the material best suited for an arched bridge. It combines 
great resistance to compression or strength, with durability 
and economy ; qualifications already given as requisite for an 
engineering structure. 

Wrought! iron is sometimes used for arched bridges. Where 
the bridge is liable to considerable transverse strains or shocks, 
it would be a better material than cast iron to be used. 

490. Construction. — Instead of the soffit being a continu- 
ous surface, as in the masonry arch, it is formed, in the iron 
arch, of curved iron beams placed side by side at suitable 
distances apart, and bound together by lateral bracing. This 
lateral bracing to bind the ribs together, and the proper abut- 
ting of the ends of the ribs, and the fastening of them upon 
the bed-plates or skew-backs of the abutments, form the most 
important part of the construction. 

The ribs are generally made in segments, the joints being 
in the direction of the radii of curvature of the under surface 
of the rib. To guard against any possibility of accident, the 
segments are bolted together at the joints, forming in this 
way a continuous curved beam. 

The form of the under surface of the rib is either parabolic 
or circular, more generally the latter. The rise is taken 
ordinarily at about -^th of the span. 



^ -i «yi 




Fig. 194. 



The rib may be solid, having cross-section of the usual 
x-shape, the upper and lower flanges being equal ; or it may 
be tubular ; or it may be open-work, similar to a truss in which 
the chords are curved. 

The first is the usual form. The other forms have been 
and are frequently used, but require no particular description. 



ARCHED BRIDGES. 371 

Whatever be the form of cross-section of the rib, it is usual 
to place along the crown a horizontal beam, generally of 
wrought iron, suitably stiffened by covering plates and angle- 
irons." (Fig. 194.) 

The connection of this beam with the curved rib is made 
by a truss-work, called the spandrel filling, as shown in the 
figure. 

On the horizontal beams the roadway is placed. 

491. Expansion and contraction. — The rib is frequently 
hinged at the crown and ends, and sometimes at the ends 
only, to provide for the expansion and contraction of the 
metals produced by changes of temperature. 

It is a matter of doubt whether anything is gained by this 
provision, as the friction arising from the great pressure on 
the joint probably prevents the necessary motion of rotation 
to relieve the arch from the increased strain. 

512. Arched bridges of steel. — Bridges of this class, 
made of steel, do not differ in principle from those in iron. 
The most noted example of the steel arch is that used in the 
St. Louis and Illinois Bridge, across the Mississippi River, 
at St. Louis, Missouri. 

In this bridge, that which corresponds to the rib, in the 
previous descriptions, is composed of two tub alar steel ribs 
placed directly one over the other and connected by a truss- 
work. 

The segments of eadi of the tubular ribs are straight 
throughout their length, instead of being curved. The ends 
of each segment are planed off in the direction of the radius 
of curvature, and abut against the ends of the adjacent seg- 
ment, to which they are joined and fastened. In this way 
the tube is made continuous ; but instead of being curved, it 
is polygonal, as in the case of the bowstring girder. The 
tubes are connected bj a truss-work, and the whole forms a 
rib of the third class. 

493. Eads' patent arch bridge. — Captain Eads, the en- 
gineer of the St. Louis Bridge, has patented an arch bridge, 
the principle of which is shown in Fig. 195. 

This arch is hinged at the crown, C, and springing lines, 
A and B, to provide for the expansion and contraction of the 
metal used in its construction. This arrangement of hinging 
the arch at the crown reduces the construction to that of two 
inclined beams resting against each other at C. Each beam 
is a truss belonging to the triangular system and having curved 
chords. 

The line, A C B, is the arc of a parabola, wdiose vertex is 



372 



CIVIL ENGINEERING. 



at C. The lines, ADC and CEB, are also arcs of parabolas. 
The maximum depth of either truss must not exceed one-half 
the rise of A C B. 




Fig. 195. 

494. Cases in which the arch may "be preferred to the 

truss. 

The arch will usually be found to be a less expensive struc- 
ture than the truss, when the banks are of rock forming good 
natural abutments. 

It will oftentimes be more economically employed where a 
deep valley is to be spanned and where high arches can be 
used. 

It is to be preferred when the roadway is a very heavy one, 
as in the case of a macadamized, or similar covering. 

It is frequently selected in preference to a truss, from 
architectural considerations. 



CHAPTER XYII. 



SUSPENSION BRIDGES. 



495. A suspension bridge is one in which the roadway 
over the stream or space to be crossed is suspended from 
chains or wire ropes. The chains or wire ropes pass over 
towers, the ends of the chains being securely fastened or 
"'anchored " in masonry at some distance behind and below 
the towers. The roadway, usually of wooden planking, is 



SUSPENSION BRIDGES. 



373 



supported by suspending rods placed at regular distances 
(Fig. 196.) 



alono- the chains. 




Fig. 196. 

Suspension bridges are used principally for spans too great 
to be crossed by arches or trass-work at a reasonable cost. 
Sometimes they are used, where the span is not very great, 
as a roadway only for foot passengers, especially over high- 
banked rivers, ravines, and similar places where the cost of a 
bridge of the other kinds would be oat of proportion to the 
service required. 

496. A suspension bridge consists of the towers or piers, 
over which the main chains or cables pass ; the anchorages, 
to which the ends of the cables are attached ; the main chains 
or cables, from which the roadway is suspended ; the sus- 
pending rods or chains, which connect the roadway with 
the main chains ; and the roadway. 

497. Towers. — The towers, frequently termed piers, are 
made generally of masonry, although iron has sometimes been 
used. The particular form of the towers will depend in a 
measure upon the locality and the character of the surround- 
ings. The dimensions to give them 
will depend upon their height and the 
amount of strains which they will 
have to resist. 



Their construction will be governed 



Oft oo 



by the rules already given for the 
careful construction of masonry. 

A cast-iron saddle on rollers, to allow 
of free motion in the direction of the 
length of the main chains, is placed 
on each tower. (Fig. 197.) 

The main chains may be fastened to these saddles, but they 
are generally passed over them. 




Fig. 197. 



374: CIVIL ENGINEERING. 

The strains on the towers are produced by the vertical and 
horizontal components of the tensions in the cables. 

The tower must be built expressly to resist the crushing 
forces due to this vertical component of the tension and the 
weight of the masonry. 

If the saddle was not free to move, the horizontal force 
tending to push the tower over would be equal to the differ- 
ence of the horizontal components of the tension in the two 
branches of the main chain. But since the saddle, by means 
of the rollers, is free to move, the only horizontal force acting 
at the top of the tower is that which comes from the friction 
of the rollers. 

498. Anchorage. — If the shore or bank be of rock, a ver- 
tical passage should be excavated and a strong iron plate 
placed in the bottom and firmly imbedded in the sides of the 
passage. Through this plate the ends of the main chains are 
passed and firmly secured on the under side. After the 
chains are put in place the passage should be filled with con- 
crete and masonry. 

If the rock is not suitable, a heavy mass of masonry should 
be built of large blocks of cut stone, well bonded together 
for this purpose. In this case it is advisable to construct a 
passage way, so that the chains and the fastenings may be 
examined at any time. This mass of masonry, or the natural 
rock to which the ends of the chain are fastened, is frequently 
called the abutment. Its stability must be greater than the 
tension of the chains. The principles of its stability are 
precisely the same as those for the abutment of an arch; its 
weight and thickness must be sufficient to prevent its being 
overturned ; and its centre of resistance must be within safe 
limits. 

499. Main chains or cables. — These may be made of 
iron bars, connected by eye-bar and pin joints; of iron links, 
as in common chains ; of hoop or strap iron ; of ropes or 
cables of wire, and in some cases of vegetable fibre, as hemp, 
flax, or bark. When of ropes or strap iron they are of 
uniform cross-section; when of links they may have variable 
cross-sections. 

The smallest number of cables in a suspension bridge is 
two, one to support each side of the roadway. Generally 
there are more than two, since, for the same amount of 
material, they offer at least the same resistance, are more 
accurately manufactured, less danger of accident, and can be 
more easily put in place and replaced than a single chain of 
an equal amount of material. 



SUSPENSION BRIDGES. 375 

Discussions have arisen as to the respective advantages 
possessed by the chain and wire cables, some engineers pre- 
ferring the former to the latter, and the reverse. The wire 
cable is generally adopted in the United States. 

The wire cable is composed of wires, generally from -Jth 
to -J-th of an inch in diameter, which are brought into a cylin- 
drical shape by a spiral wrapping of wire. Great cart; is 
taken to give to each wire in the cable the same degree of 
tension. 

The iron wires are coated with varnish before they are 
bound up into the cable, and when the cable is completed 
the usual precautions are taken, as in other iron-work, to 
protect it from rust and the action of the weather. 

If the load placed on a cable be a direct function of its 
length, the curve assumed by the mean fibre of the cable will 
be a catenary. If it be a direct function of the span, it will 
be a parabola. But the weight resting on the main chains is 
neither a direct function of the length of the cable, nor of 
the span, but a function of both. The curve is therefore 
neither a catenary nor a parabola. But since the roadway, 
which forms the principal part of the load, is distributed very 
nearly uniformly over the span, the curve approaches more 
nearly the parabola and in practice is taken to be that 
curve. 

Knowing the horizontal distance between the tops of the 
towers and the deflection, the corresponding length of the 
cable between the two points of support may be obtained by 
the operation of rectifying the curve of a parabola. (Church' s 
Integral Calculus, Art. 235.) The length obtained by this 
method will be expressed in terms containing logarithmic 
functions. For this reason approximate formulas are made 
which will give the length, in most cases, near enough for 
practical purposes. Rankine gives the following approxi- 
mate value for the length of a parabolic arc : 

s = x + | y - {nearly). . . (162). 

Where the cable is to have a constant cross-section through- 
out, the area of this section must be proportioned to the 
greatest tension upon the cable. This tension is greatest at 
the points of support when they are of the same height, or 
at the highest point when the heights are unequal. 

If the main chain is made of bars or links, it may be pro- 
portioned to form a chain of uniform strength, in which case 
the cross-sections will be made to vary from the lowest point 



376 CIVIL ENGINEERING. 

to the highest, increasing in area of cross-section as the strain 
of tension increases. The horizontal component, or tension 
of the lowest point, is dependent upon the parameter of the 
curve. It therefore follows that for the same curve and the 
same load on the unit of length throughout, the horizontal 
component is the same for a bridge of a span of ten as for 
one of a thousand feet. And it is also plain that the wider 
the span, the deflection remaining constant, the greater will 
be the tension on the cable, and the reverse. 

500. Suspending 1 chains. — The roadway is suspended 
from the cables by wire ropes or iron rods, which are placed at 
equal distances along the cable, for the purpose of distributing 
the load as nearly uniformly as possible over the cables. 

If the cables are composed of links or bars, the suspending 
rods may be attached directly to them. If of rope, either 
wire or vegetable material, the suspension rod is attached to 
a collar of iron of suitable shape bent around the cable, or to 
a saddle-piece resting on it. 

Where there are two cables, care must be taken to distribute 
the load held by the suspension rod upon the cables accord- 
ing to their degree of strength. 

In the ITungerford Suspension Bridge the method adopted 
was as follows : The suspension rod, A (Fig. 198), was at- 
tached to a triangular plate, B, 
which hung by the rods, C and 
D, from the main chain, E and 
F. By this arrangement half 
of the load on the rod, A, was 
supported by each of the main 
chains, E and F. 

The suspending rods may 
be vertical or inclined. In 
recent constructions they are 
Fig. 198. frequently inclined inwards, 

for the purpose of giving ad- 
ditional stiffness to the framing. The, cross-section of the 
rod is constant, and is determined by the amount of strain on 
the upper section. 

501. Roadway. — The roadway in its construction does 
not differ in principle from that used for other forms of 
bridges. The roadway bearers are supported by the suspen- 
sion rods. Longitudinal joists are laid, and on them the 
planking, or the planking is laid directly on the roadway 
bearers. The latter are "stiffened bv diagonal tics of iron 
placed horizontally between each pair of roadway bearers. 




SUSPENSION BRIDGES. 



377 



502. Oscillations. — Suspension bridges, from the nature 
of their construction, are wanting in stiffness, and hence are 
peculiarly liable to both vertical and horizontal oscillations, 
caused by moving loads, action of winds, etc. 

These oscillations cannot be entirely prevented, but their 
effect may be reduced so as to be almost harmless. 

When the banks will admit of it, guy-ropes of wire may 
be attached to the roadway and fastened to points of the 
bank beneath the bridge. The guy-ropes directly under the 
bridge will be the most effective in resisting the vertical 
oscillations; those oblique to the bridge, for resisting the 
horizontal. 

The elder Brunei fastened the roadway to a set of chains, 
reversed in form to that of the main chains. The reversed 
chains had a cross-section of about one-third of the main 
chains, and preserved the shape of the roadway under a 
movable load even better than by means of guys. 

Engineers have made many efforts to provide for this 
want of stiffness in suspension bridges and fit them for rail- 
road uses. 

A heavy moving load coming on a suspension bridge, 
when at a point, as M (Fig. 19U), causes the roadway and 
cables to assume positions similar to those indicated by the 




Fig. 199. 



dotted lines in the figure. To prevent this deformation, the 
cables are fastened at the points of greatest change by chains, 
A E and B F, attached to the piers. These are 'known as 
Ordish's chains. 

Roebling effected the same thing by fastening these points 
of change in the roadway to the top of the towers, by the 
lines, Da, Db, etc., as shown in Fig. 200. 

It is agreed at the present time that the best method of 
increasing the stiffness of a suspension bridge is to use, in 
addition to the chains just named, trussed parapets on each 
side of the roadway. These parapets form two open-built 
beams, strongly connected and braced by the roadway, and 



378 



CIVIL ENGINEEKING. 



supported at intermediate points by the attachments to the 
main chains. Each end of the roadway is firmly secured to 
the base of the tower. 




Fig. 200. 

The objection to this method is the increase of weight 
placed upon the main chains. 

503. Niagara Suspension Bridge. — This bridge was 
planned and constructed by Roebling, and illustrates the 
method of stiffening just named. 

It affords a passage-way over the Niagara River, a short dis- 
tance below the Falls, both for a railroad and a common road. 
It consists of two platforms (Fig. 201). one above the other, 



..24.'. 




Fig. 201. 



and about fifteen feet apart ; the upper is for the railroad 
track, and the lower, B, is for the common road. The plat- 
forms arc connected by a lattice truss-work, C, C, on each 
side, which serves to increase its stiffness. The whole bridge 
is suspended by four main wire cables, F, F, F', F', the upper 



NIAGARA SUSPENSION BRIDGE. 



879 



two "being connected with the upper platform, and the lower 
two with the lower platform. 

Each platform consists of a series of roadway bearers in 
pairs ; the lower covered by two thicknesses of flooring- 
plank, the upper by one thickness ; the portion of the latter 
immediately under the railroad track having a thickness of 
four inches, and the remainder on each side out two inches. 

The roadway bearers and flooring of the upper platform 
are clamped between four solid-built beams ; two above the 
flooring, which rest on cross supports ; and two, correspond- 
ing to those above, below the roadway bearers ; the upper 
and lower corresponding beams, with longitudinal braces in 




Fig. 202. 



pairs between the roadway bearers and resting on the lower 
beams, being firmly connected by screw-bolts. The rails are 
laid upon the top beams, forming the railroad track, A. A 
parapet, D, D, of the form of the Howe truss is placed on 
each side. 

The lattice-work, C, C, which connects the upper and 
lower platforms, consists of vertical posts in pairs (Figs. 202), 

rods, T, T. The rods pass 



and of diagonal wrought-iron 



380 



CIVIL ENGINEERING. 



through cast-iron plates fastened above the roadway bearers 

of the upper platform, and below those of the lower, and are 

brought to a proper bearing by nuts and screws on each end. 

A horizontal rail of timber is placed between the posts of the 

lattices at their middle, to prevent flexure. 

The towers (Fig. 203) are 
four obelisk-shaped pillars, each 
sixty feet high, with a square 
base of fifteen feet on a side, 
and one of eight feet at the 
top. 

The height of the pedestals on 
the Canada side is eighteen feet, 
and on the United States twenty- 
eight. An arch, C, connects 
the two pedestals, under which 
is a carriage-way, D, for com- 
municating with the lower plat- 
form. 

The. main cables pass over 
saddles on rollers placed on tops 

*fc'....„l.„./jff&1_„l 1 J of the towers, and are fastened 

Fig. 203. at their ends (Fig. 204) to chains 

made of iron bars attached to an 

anchoring plate, D, of iron, firmly secured in an anchorage of 

rock, B, and a mass of masonry, A. 





Fig. 204. 

The upper set of main cables are drawn in towards the 
axis of the bridge to reduce the effect of horizontal oscilla 



MOVABLE BRIDGES. 381 

tions. This arrangement of the cables, the parapet on the 
upper platform, the lattice work joining the two platforms, 
the guy-ropes from the banks and the chains from the tops 
of the towers, the deep continuous beams of the railroad 
track, the camber given to the roadway, and the weight of 
the structure, all give it a degree of stiffness and stability 
that has rendered it very successful as a railroad bridge. 

The following are some of the principal dimensions: 

Span of the cables, 821^- feet. 

Length of roadway between piers, 800 feet. 

Deflection of upper cables (mean temperature), 54 feet. 

Deflection of lower cables " " 64 feet. 

Length of upper cables " " 1,193 feet. 

Length of lower cables " " 1,261 feet. 

Ultimate strength of the four cables, 12,000 tons. 

Permanent weight supported by cables, 1,000 tons. 

Tension on four cables, 1,810 tons. 

Height of railroad track above mean stage of water, 245 
feet. 

504. East River Suspension Bridge. — This bridge is in 
process of construction, and when completed will have a span 
of 1,595 \ feet. The centre of the span will be 135 feet 
above mean high tide. There are to be four cables, each 16 
inches in diameter, made of steel wire. The weight of the A 3 £ 
bridge is estimated at 5,000 tons. , 



CHAPTER XYIII. 

MOVABLE AND AQUEDUCT BRIDGES. 

505. Movable bridges.— In bridges over navigable rivers 
it is often necessary that one or more spans be made to open 
to allow of the passage of vessels. The term, movable 
bridge, is therefore applied to any arrangement, whatever 
be its nature, by means of which the roadway can at pleasure 
be made continuous or broken, between two points of a 
permanent bridge, or over a water-way. The methods used 
to effect this are various. 

They may be classed under five heads : 



382 CIVIL ENGINEEKING. 

1, The passage may be opened or closed by turning a 
portion of the bridge around a vertical axis ; 2, by turning 
it around a horizontal axis ; 3, by making it roll forwards 
and backwards in a line with the bridge ; 4, by lifting it 
vertically above the passage ; and 5, by floating it from and 
into place upon the water. 

506. I. By turning around a vertical axis. — The term, 
swing- bridge, is generally applied to a bridge which turns 
about a vertical axis. It is the form of bridge most generally 
used when the opening is of any size. If two openings 
are required, the bridge rests upon a masonry pier, midway 
between the openings, which supports a circular plate, the 
diameter of which is equal, or nearly equal, to the breadth 
of the bridge. This plate has a pivot in the centre and a 
circular track with rollers around the circumference. On 
this pivot the bridge is revolved horizontally, being turned 
by suitable machinery. 

If only one opening is required, the abutment is generally 
used to support the -mechanism for turning the bridge, care 
being taken to place the pivot far enough back from the face 
of the abutment so that, when the bridge is parallel to this 
face, it shall not project beyond it. 

In calculating the strains on the parts of such a bridge, it 
as usual to consider it, when open, as two cantilevers loaded 
with its own weight, and, when closed, as the spans of a 
bridge under ordinary circumstances. 

507. II. By turning around a horizontal axis. — Where 
the width of the opening is small, the moving portion of the 
bridge, which may be in one or two pieces, is lifted by chains 
attached to the extremities, the operation being assisted by 
counterpoises connected with the mechanism used for lifting. 
One of the simplest counterpoises is that of a lever revolving 
on a horizontal axis above the bridge, one end of the lever 
being connected with the movable end of the bridge by a 
■chain, and the other weighted and connected with the 
mecjianism by which the bridge is lifted. 

508. III. By moving a portion of the bridge forward 
and backward in a line with its axis. — Bridges of this 
kind are placed upon fixed rollers, so that they can be moved 
forward or backward, to interrupt or open the communication 
across the water-way. The part of the bridge that rests upon 
the rollers, when the passage is closed, forms a counterpoise 
to the other. The mechanism usually employed for moving 
these bridges consists of tooth-work, and may be so arranged 
that it can be worked by one or more persons standing on the 



AQUEDUCT BRIDGES. 383 

bridge. Instead of fixed rollers turning on axles, iron balls 
resting in a grooved rolleivway may be used, a similar roller- 
way being affixed to the frame-work beneath. 

Bridges of this class are known as rolling- bridges. 

509. IY. By lifting - . — In small bridges, like those over 
canals, the bridge is sometimes hung by the four corners to 
chains which pass over pulleys and have counterpoises at the 
other ends. A slight force applied to it raises the bridge 
to the required height, allowing the boats to pass under the 
bridge. 

510. Y. By floating. — A movable bridge of this kind may 
be made by placing a platform to form a roadway upon a 
boat or a water-tight box of a suitable shape. This bridge is 
placed in or withdrawn from the water-way, as circumstances 
may require. 

A bridge of this character cannot be conveniently used in 
tidal waters, except at certain stages of the water. It may 
be employed with advantage on canals in positions where a 
fixed bridge could not be placed, in which case a recess in 
the side of the canal is made to receive it when the passage- 
way is opened. 

511. The general term, draw-bridge, is applied to all 
these movable bridges, although technically the term is con- 
fined to bridges of the second class, or those revolving 
around a horizontal axis. 

Movable bridges are either simple bridges or made of 
truss-work belonging to one of the three systems already 
named. 

The objections to a movable bridge belonging to either of 
the other three classes of bridges are apparent. Where 
either of these classes is used, the passage-way can only be 
kept open by constructing the bridge so that a vessel can pass 
beneath it. 

512. Aqueduct "bridges. — In aqueducts and aqueduct 
bridges of masonry, for supplying a city with water, the 
volume of water conveyed being comparatively small, the 
structure will present no peculiar difficulties beyond afford- 
ing a water-tight channel. This may be made either of 
masonry, or of cast-iron pipes, according to the quantity of 
water to be delivered. If formed of masonry, the sides and 
bottom of the channel should be laid in the most careful 
manner with -hydraulic cement, and the surface in contact 
with the water should receive a coating of the same material, 
particularly if the stone or brick used be of a porous nature. 
This part of the structure should not be commenced until the 



384 CIVIL ENGINEERING. 

arches have been imcentered and the heavier parts of the 
structure have been carried up and have had time to settle. 
The interior spandrel-filling, to the level of the masonry 
which forms the bottom of the water-way, may either be 
formed of solid material, of good rubble laid in hydraulic 
cement, or of concrete ; or a system of interior walls, like 
those used in common bridges for the support of the roadway, 
may be used in this case for the masonry of the water-way to 
rest on. 

In aqueduct bridges of masonry, supporting a navigable 
canal, the volume of water is much greater, and every pre- 
caution should be taken to procure great solidity, and secure 
the structure from accidents. 

Segmental arches of medium span will generally be found 
most suitable for works of this character. The section of the 
water-way is generally of a trapezoidal form, the bottom line 
being horizontal, and is usually, for economy, made wide 
enough for one boat only. On one side of the water-way is 
a tow-path for the horses, and on the other a narrow foot- 
path. 

The principle of the suspension bridge is well adapted to 
aqueduct bridges, because, as each boat displaces its own 
weight of water, the only moving load is the passage of men 
and horses along the tow-path. 



CHAPTER XIX. 

BRIDGE CONSTRUCTION. 

513. Before a bridge can be constructed there are three 
things to be considered, viz., 1st, the site ; 2d, the water-way ; 
3d, the design or plan. 

Before a bridge can be designed a thorough knowledge of 
the site, the amount of water-way, and the particular service 
required of the bridge, must all be known. 

514. Site. — The site may already be determined, and it, 
may not be in the power of the engineer to change it. If it 
is in his power to locate the site within certain limits, ho 
will select the locality which offers the most security for the 



BRIDGE CONSTRUCTION. 385 

foundations and the least expense to be incurred in their 
construction and that of the bridge. 

In many eases it is a matter of indifference where the 
stream is crossed, but a careful survey of the proposed site 
should always be made, accompanied by borings. The 
object of this survey is to ascertain thoroughly the natural 
features of the surface, the nature of the subsoil of the bed 
and banks of the water-course, and the character of the 
water-course at its different phases of high and low water, 
and of freshets. This information should be embodied in a 
topographical map; in cross and longitudinal sections of the 
water-course and the substrata of its bed and banks ; and in 
a descriptive memoir which, besides the usual state of the 
water- course, should exhibit an account of its changes, occa- 
sioned either by permanent or by accidental causes, as from 
the effects of extraordinary freshets, or from the construction 
of bridges, dams, and other artificial changes either in the 
bed or banks. 

Having obtained a thorough knowledge of the site, the 
two most essential points next to be considered are to adapt 
the proposed structure to the locality, so that a sufficient 
water-way shall be left both for navigable purposes and for 
the free discharge of the water accumulated during high 
freshets; and to adopt such a system of foundations as will 
ensure the safety of the structure. 

515. Water-way. — "When the natural water-way of a 
river is obstructed by any artificial means, the contraction, if 
considerable, will cause the water, above the point where the 
obstruction is placed, to rise higher than the level of that 
below it. This difference of level is accompanied by an in- 
crease of velocity in the current of the river at this place. 
This damming of the water above the obstruction, and in- 
crease of velocity in the current between the level above and 
the one below the obstruction, may, during heavy freshets, 
cause overflowing of the banks; may endanger, if not 
entirely suspend, navigation during the seasons of freshets ; 
and expose any structure which, like a bridge, forms the 
obstruction, to ruin, from the increased action of the current 
upon the soil around its foundations. 

If on the contrary, the natural water-way is enlarged at 
the point where the structure is placed, with the view of pre- 
venting these consequences, the velocity of the current 
during the ordinary stages of the water will be decreased, 
and this will occasion deposits to be formed which, by gradu- 
ally filling up the bed of the stream, might prove, on a sudden 
25 



386 CIVIL ENGINEERING. 

rise of the water, a more serious obstruction than the struc- 
ture itself; particularly if the main body of the water 
should happen to be diverted by the deposit from its 
ordinary channels, and form new ones of greater depth 
around the foundations of the structure. 

For these reasons, the wa^er-way to be left after the bridge 
is built should be so regulated that no considerable change 
shall be occasioned in the velocity of the current through it 
during the most unfavorable stages of the water. 

The beds of rivers are constantly undergoing change, the 
amount and nature of which depend upon the kind of soil of 
which they are composed, and the velocity of the current. 

516. The following table shows, on the authority of Du 
Buat, the greatest velocities of the current close to the bed 
without injury to or displacement of the material of which it 
is composed : 

Soft clay 0.25 feet per second. 

Fine sand 0.50 " " 

Coarse sand and fine gravel.. . 0.70 " " 

Gravel, ordinary 1.00 " " 

Coarse gravel, 1 in. in diameter 2.25 " " 

Pebbles, 1|- in. in diameter. . . 3.33 " " 

Heavy shingle 4.00 " " 

Soft rock, brick, etc 4.50 " " 

Rock \ 6 - 00 " " 

( and greater. 

Knowing the material of which the bed of the river at 
the site is composed, and regulating the water-way so that 
the velocity of the current close to the bottom after the 
bridge has been erected, during the heaviest freshets shall 
not exceed the limit of safety or disturbance of the material 
forming the bed, the stability of the foundations is assured. 
If the velocity should exceed the limits here given, precau- 
tions must be taken to protect the foundations, as heretofore 
described. 

517. Velocity. — The velocity of a current depends upon 
the slope of the bed. Since the particles of water in contact 
with the earth of the sides and bottom of the stream are 
retarded by friction, it follows that in any cross-section the 
velocity of the particles in the centre differs from these at. 
the bottom and on tl^e sides. In ordinary cases it is suffi- 
ciently exact to take the least, mean, and greatest velocities 
as being nearly in the proportions of 3, 4, and 5; and for 
very slow currents they are taken to be nearly as 2, 3, and 4. 



WATER-WAY. 387 

The greatest velocity may be obtained by actual measure- 
ment, by means of floats, current metres, or other suitable 
apparatus, or it may be calculated from the slope of the bed 
of the river at and near this locality. 

Having determined the greatest velocity, the mean velocity 
is taken as four-fifths of it. Col. Medley, in his Treatise on 
Civil Engineering, takes the mean velocity as nine-tenths 
(nearly) of the surface velocity when the latter exceeds three 
feet per second, and four-fifths when less than this. 

Having determined the mean velocity of the natural water- 
way, that of the contracted water-way may be obtained from 
the following expression, 

a 

v = m—V, (163) 

s 

in which s and v represent, respectively, the area and mean 
velocity of the contracted water-way ; S and Y, the same 
data of the natural water-way ; and m a constant, which, as 
determined from various experiments, may be represented by 
the number 1,045. 

Giving to s a particular value, that for v may be deduced, 
which may then be compared with the velocity allowable at 
this locality ; or, assuming a value for v, the value of s may 
be deduced, which will fix the area of the contracted water- 
way. The safest width, or area of water-way, in many cases 
may be inconveniently great ; therefore, some risk must be 
run by confining the floods to more contracted limits. To 
reduce this risk as much as possible is the object of the 
engineer in seeking this information. With this information, 
the engineer can decide upon the number of piers, hence the 
number of spans of the bridge. Knowing the nature of the- 
bottom, the character and- kind of piers and abutments may 
be selected. 

518. Design or plan of "bridge. — Before the engineer can; 
complete the design of the bridge, it is necessary that he 
should know what service it has to perform : whether it is to 
be a common or a railroad bridge ; whether a single or double- 
track one. This being given, and the knowledge acquired of 
the site and water-way furnished him,, he is able to decide 
whether the structure shall be a truss, arched, or suspension 
bridge ; and, knowing the facilities at the place for the con- 
struction of the work, can prepare an estimate of its probable 
cost. 

In deciding on the form of bridge which shall best com- 
bine efficiency with economy, there (1 are many tilings to be 



388 CIVIL ENGINEERING. 

considered. The cost of the superstructure, or all above the 
piers and abutments, increases rapidly with the length of 
span. Hence, economy would, as far as the superstructure is 
concerned, demand short spans. But short spans require an 
increase in the number of piers. When the height is small. 
the stream not navigable, and the piers easy to build, short 
spans may be used ; but, if the foundations are in bad soils, 
if the river is deep, with a rapid current, or liable to great 
freshets, if it is navigable and requires an unobstructed 
water-way, the construction of piers will be very expensive, 
and therefore it is often desirable in these cases that there 
should be few or no piers in the stream ; hence, long spans 
are necessary, even at great cost. Good judgment and accu- 
rate knowledge on the part of the engineer will be necessary, 
in order that these and similar questions should be decided 
correctly; 

ERECTION OF BRIDGE. 

519. The bridge having been planned, its parts all prepared 
.and taken to the site, the abutments and piers built, the next 
step is to put it in position. 

There are three methods, which have already been named, 
viz., building the bridge on a scaffolding in the position it is 
to occupy; building it arid rolling it in position, known as 
launching / and building away from the site and then float- 
ing it to the spot, and lifting it in place. 

520. Scaffolding. — The scaffolding is, so far as principle 
is concerned, the same as that already described under the 
head of masonry. That used for bridge construction is 
simply a rough but rigid trestling, resting on the ground, or 
on piles when the scaffolding is over water. The whole 
arrangement is sometimes called staging, and frequently 
false-works. 

By means of this scaffolding the different pieces of the 
structure are lifted in place and fastened together. When 
the bridge is finished the staging is removed. This method 
is the one most generally used. 

521. Launching. — This method has been used where the 
scaffolding would have been too great an obstruction to the 
stream or too costly. Deep and rapid rivers or ravines, 
where the bridge is erected at a very high level, or rivers 
with rapid currents subject to great freshets, are cases 
where scaffolding would be costly, and in some cases imprac- 
ticable. 



COST OF BRIDGE. 389 

522. Floating to site and lifting in place. — This 
method has been used in connection with the last method. 

In this method the truss or tube is placed on boats or 
pontons, and floated to the spot it is to occupy. Then, by 
cranes or other suitable lifting machinery, the truss is lifted 
to its place. This was the method adopted for the Britannia 
Tubular Bridge. 

In tidal waters this method has been used with great 
success. The truss was put together on platforms on' the 
decks of barges, at a sufficient height above the surface of 
the water, so that at high tide the truss would be above the 
level of its final position. The barges were then floated into 
position at high tide, and as the tide fell the truss was de- 
posited in its proper place. 

523. Cost. — The cost of erecting a bridge is divided gene- 
rally into four parts: 1, Scaffolding ; 2, Plant; 3, Labor; 
4, Superintendence. 

Scaffolding-. — The cost of this forms an essential part of 
the estimate, and depends greatly upon the facilities for 
obtaining the proper materials in the vicinity of the site. 

Plant. — This is a technical word used to include the tools 
and machinery employed in 3 the work. The employment of 
steam in so many ways at the present time renders this item 
an important one in estimating the cost. 

Labor — The number of men, their wages, subsistence, and 
oftentimes their transportation, have all to be considered 
under this head. 

Superintendence. — Good foremen and able assistants are 
essential to a successful completion of the work. Their wages 
may be included in the last item. It is usual to allow a given 
percentage on the estimate to include the cost of superintend- 
ence. 

Summing these four items together, the cost of erecting 
the superstructure of the bridge may be estimated. 



PART VII. 



CHAPTEE XX. 

ROOFS. 

524. The term roof is used to designate the covering 
placed over a structure to protect the lower parts of the 
building and its contents from the injurious effects of the 
weather; It consists of two distinct parts — the covering and 
the frames which support the covering. By some the term 
roof is applied only to the " covering," exclusive of the 
frames. 

525. Roofs are of various forms — angular, curved, and 
flat, or nearly so. 

The most common form of roof is the angular. These 
vary greatly in appearance and in construction. Some of the 
most common examples of the angular roof are the ordinary 
gabled, the hipped, the curb or Mansard, the French roof, 
etc, 

Curved roofs and dome's are frequently used. They cost 
more than the angular roofs, if the cost of the abutments be 
included. But if the abutments exist or for other reasons 
they have to be built, the curved roof, under these circum- 
stances, in many cases, may be found cheaper and more suit- 
able. 

Flat roofs are very common, especially in hot climates. 
The covering of these roofs rests upon beams placed in a 
horizontal position, or one that is nearly so. The slope given 
them is generally about 4° with the horizontal. 

These roofs are easy to construct, and are simple in plan, 
but they arc heavy, do not allow the water to escape freely, 
and there is a waste of material. 

5ii(>. Coverings. — The coverings of roofs are made of 
boards, shingles, slates, mastics, tho metals, or any suitable 



ROOFS. 391 

material which will stand exposure to the weather and afford 
a water tight covering. The style of the building, and the 
especial object to be attained, will govern their selection. 
Tiie extent of surface covered by them is usually expressed 
in square feet. Sometimes the term square is only used, in 
which case it means an area of 100 square feet. 

The weight of the materials used for the covering is about 
as follows : 

Material. Weight per square foot. 

Copper 1 lb. 

Lead 7 lbs. 

Zinc 1.5 lbs. 

Tin fib. 

Iron (common) 3 lbs. 

Iron (corrugated) 3.5 lbs. 

Slates 5 to 12 lbs. 

Tiles 7 to 18 lbs. 

Boards, 1 inch thick 2-| lbs. 

Shingles 1 lb. 

These are fastened directly upon the frames, or upon 
pieces of scantling and boarding which rest on the frames. 

527. Frames. — The frames which support the covering 
have their exterior shape to correspond to the form of the 
roof. These frames, known generally as roof-trusses, are 
tied together and stiffened by braces which may occupy 
either a horizontal or inclined position, and may be either 
notched upon or simply bolted to the trusses. 

The trusses are placed from five to ten feet apart, depend- 
ing upon the weight of the covering and the amount of load 
which each truss has to support. They rest usually upon 
pieces of timber called -wall-plates, laid on the wall to 
distribute the pressure transmitted by the truss over a larger 
surface of the wall. 

528. Although nearly the last part of a building which is 
constructed, the roof is one of the first to be considered in 
planning the building, since the thickness and the kind of 
wall depend greatly upon the weight of the roof. The 
weight of the roof and the size of the pieces to be used in its 
construction, when the roof is flat, are easily determined. 
The pieces are simple beams, subjected only to cross-strains, 
and the joints are of the simplest kind. 

When the roof is curved or inclined, these determinations 
are more difficult. In these roofs the strains on the parts 
produced by the covering are of different kinds, and must be 



392 CIVIL ENGINEEEING. 

determined completely, both in amount and kind, before the 
dimensions of the different pieces can be fixed, and the best 
form of joints and fastenings selected. 

In calculating the strains on a roof-truss, we must take 
into consideration, besides the weight of the covering and of 
the truss itself, the weight of the snow, ice, or water which 
may at times rest upon the covering, the effect due the action 
of the wind, and such extra loads as the weight of a ceiling, 
of machinery, of floors, etc., which may be supported by the 
frames. 

The weight of the covering varies, as has been shown, 
from one pound to twenty pounds upon the square foot. 
The weight of the truss increases with the span, but it is 
only in very wide spans that the weight of the parts and of 
the whole truss have to be considered. 

The weight of snow is assumed to be about one-tenth that 
of the same bulk of water. Knowing the maximum depth 
of the falls of snow, an approximate weight maj be deter- 
mined. Six pounds per square foot is the estimated weight 
of snow adopted by European engineers. A greater weight, 
even as high as twenty pounds, is recommended for the 
northern part of the United States. 

The action of the wind is very great in some localities. 
Tredgold recommends an allowance of forty pounds to the 
square foot as an allowance for its effect. 

529. Rise and span. — These are quantities dependent 
upon circumstances. The rise is dependent upon the kind of 
roof, the order of architecture used for the building, and the 
climate. The span is dependent upon the size of the 
building. 

In gabled roofs and ordinarily angled roofs, the inclina- 
tion which the sides of the roof make with the horizontal is 
called the pitch. In countries where heavy falls of snow 
are common the pitch is ordinarily made quite steep — al- 
though builders are now more generally inclined to a mode- 
rate pitch, even for these cases. The objections to a steep 
pitch are the exposing of a greater surface of the roof to the 
direct force of the wind, the waste of room, etc. The mate- 
rial of which the covering is composed affects the pitch. An 
ordinary roof covered with shingles should have a pitch of at 
least 2 2-£ degrees ; one covered with slate or tiles a pitch 
something greater, between 23 and 30 degrees. 

The style of roof and architecture affect the pitch. Gothic 
styles and parts of French roofs require a pitch of 45 degrees, 
and even of GO decrees. 



ROOFS. 



393 



530. Materials used in construction. — Wood and iron 
are the materials used for the construction of the frames. 
The truss may, as in other frames, be made entirely of wood, 
or entirely of iron, or of a combination of the two materials. 



WOODEN HOOF-TRUSSES. 



531. The simplest wooden truss is the triangular frame. 
The inclined pieces are called rafters and the horizontal one 
is termed the tie-beam. 

It is used for spans of 12 to IS feet, and when the roof 
is light. For spans of IS to 30 feet the king-post truss 
(Fig. 205) is used. Its component parts are : 




Fig. 205. 



1. The principal rafters. — These are the inclined pieces, 
B B, which abut against each other or against the king-post 
at the top. 

2. The tie-beam.— This is the horizontal beam, A, con- 
nected with the lower ends of the rafters to prevent their 
spreading out under the action of the load placed on them. 

3. The king-post. — The upright, C, framed at the upper 
end upon the rafters and connected at the lower end with the 
tie-beam. 

4. Purlins. — These are horizontal pieces, E y E, notched upon 
or bolted to the rafters to hold the frames together and to 
form supports for the common rafters, F, F. 

5. Common rafters. — These are inclined pieces, F, F, of 
smaller dimensions than the principal rafters, placed from 1 
to 2 feet apart and intended to support the covering. 

6. Struts. — The inclined pieces, D, D, framed into the 
principal rafters and king-post to prevent the rafters from 
sagging at the middle. 



394 



CIVIL ENGINEERING. 



If the king-post and struts be removed, the simple triangu- 
lar truss is left. 

532. Queen-post truss, — This truss is employed for spans 
from 30 to 45 feet long. Its parts (Fig. 206) are all shown in 
the figure ; C, C, being the queen-posts. 




Fig. 206. 



533. Iron roof-trusses. — Wooden roof-trusses have been 
used for wider spans than those named, but the use of iron in 
building has enabled the engineer to construct roof-trusses of 
wider spans which are much lighter and present a better 
appearance. 

These trusses are sometimes made of wood and iron in 
combination, as we have seen in bridge-trusses, but now they 
are more generally made entirety of iron. 

The coverings are frequently made of iron, mostly corru- 
gated, and are fastened to the purlins by the usual methods 
for iron -work. 

DETERMINATION OF THE KIND AND AMOUNT OF STRAINS ON THE 
PARTS OF A ROOF- TRUSS. 



534. Amount and kind of strains upon the different 
parts of the simple king-post truss. — The method of 
determining the amount and kind of strains on the simple 
triangular frame has already been explained. (Art. 256.) 
It is usual, except in very short spans and wdiere the tie-beam 
supports nothing but its weight, to support the middle point 
of this piece b}' a king-post. To find the strains on a tri- 
angular frame with a king-post, let A B and A C (Fig. 207) 
be the rafters, B C, the tie-beam, and A H, the king-post. The 
king-post is so framed on the rafters at A, as to hold up any 
load which it has to support. It is connected with the' tie- 
beam in such a manner as to keep the middle point, H, in the 
same straight line with B and C. 



ROOFS. 



395 



The strains on this truss are produced most usually by a 
uniform load on the rafters and a load on the tie-beam." 

Denote by £, the length of either rafter ; by w, the load on 
a unit of length, including the weight of the rafter for the 




Fig. 207. 



unit ; by TV', the weight of the tie-beam, including the load 
it has to support, as a ceiling, floor, etc., and by a, the angle 
ABC. 

The load on one of the rafters, as A B, will be wl, and acts 
through the middle point, or at a distance from B equal to il. 
The strains produced by this load are compressive on the 
rafter and tensile on the tie-beam, and the amount for each 
may be determined, as shown in Art. 254. 

The king-post is used to prevent the sagging of the tie- 
beam at its middle point. It therefore supports, besides its 
own weight, fW (Art. 186), which produces a strain of ten- 
sion on the king-post and which is transmitted by it to A, 
where it acts as a load suspended from the vertex of the 
frame. The strains produced by it on the rafters and tie- 
beam may be determined as in Art. 256. 

The strains being known in amount and kind for each piece, 
can now be summed and the total amount on the different 
parts determined. 




/f& 



535. — Strains on a king-post truss framed with struts. 

- — Let Fig. 208 represent an outline of this truss. Let D F and 
F G be the struts framed in the king-post and supporting the 
rafters at their middle points. 

The truss is supposed to be strained by a load uniformly 
distributed over the rafters. 



396 CIVIL ENGINEERING. 

Adopt the notation used in the previous case and repre- 
sent by ft, the angle A D F. AVe may neglect without 
material error the weight of the struts and king-post, their 
weights being small compared with the load on the rafters. 

The load acts vertically downwards and is equal to wl for 
each rafter. Acting obliquely, it tends to compress and bend 
them. Each rafter is a case of a beam resting on three points 
of support, hence the pressure on either strut is due to the 
action of ^wl. 

Pressure on the struts. — The pressure on the strut D F 
arises from the action of the component of $ s wl perpendicu- 
lar to the rafter at the point, D: Denote by T 1 the pressure 
on the strut in the direction of its axis. To keep the point, D, 
in the same straight line with A and B, the resistance offered 
by the strut must be equal to the force acting to deflect the 
rafter at that point. Hence there results, 

Pi sin ft = ^wl cos a. . . . (164) 

From which w r e find 

1 8 sin ft- 1 

for the pressure on the strut, D F. In the same way the pres- 
sure on the strut F G is obtained, which in this case is exactly 
equal in amount. 

Tension on king-post. — This pressure, P u is transmitted 
through the strut to the king-post at F, Resolving this force 
into its components respectively perpendicular and parallel 
to the axis of the king-post, w T e find the component in the 
direction of the axis to be Pj sin {ft — a). 

The king-post supports the tie-beam at its middle point. 
Represent as before by W, the weight of the tie-beam and 
its load, and we have fW for the pull on the king-post from 
this source. Represent the total strain of tension by T u and 
there results, 

Ti = 2P X sin (ft - a) + fW'. . . (165) 

Substituting in this for P 1? its value just found, and the 
value of T L will be known. 

Tension on the tie-beam- -Denote by T the tension on 
the tie-beam produced by the thrust along the rafters, and 
by Q, the vertical reaction at B caused by the load on the 
rafters. 

The relation between the normal components to the rafter, 



roofs. 397 

at B, of the three forces, Q, T, and -fowl acting at that point, 

may be expressed by this equation, . 

T sin a = Q cos a — -kjwl cos a. . (166) 

From which the value of T can be obtained when Q is 
known. 

Since the truss is symmetrical with respect to a vertical 
through A, the sum of the reactions at B and C, due to the 
.strains on the rafters, is 2Q, and is equal to the total load 
placed on the rafters, which is 2wl -f- f-W. Hence 

. 2Q = 2wl + | W, 
and 

Q = wl + T VW', 

which, substituting in equation (166), gives, 

T sin' a = 13 wl cos a + -&W' cos a, _ 

Strains on the rafters- — The forces acting in the direc- 
tion of the rafters produce compressive strains, and those 
perpendicular, transverse strains. These are determined as 
previously shown. 

Size of the pieces. — Having found all the strains, the 
limit on the unit of cross-section may be assumed and the 
dimensions of the pieces obtained. 

Remark. — It is well to notice, that if we substitute for 
P 1? its value in the expression for T 1? the tension on the king- 
post, that we will get 

T, = |W' + &i 221^^), 

sm /3 
which may be put under the form 

% = | |W + 2wl cos* a (l- **" |H . (168) 

It is seen from this value of T 1? that whenever ft is equal 
to 90° or differs but slightly- from it, the expression will 
reduce to the form 

T 1 = |(W / + 2wl cos 2 a). 

536. Strains on the queen-post truss. — It is easily seen 



398 



CIVIL ENGINEERING. 



from the foregoing how the strains on this truss may be de- 
termined. It is usual to suppose the truss (Fig. 209) separ- 
ated into two parts ; one the primary truss, B A C, and the 
other, the secondary trapezoidal truss, B D G C. 




Fig. 209. 



In some cases, short rafters from C to G, and B to D, are 
placed in contact with the principal rafters, A C and A B, 
which further strengthens the truss by the additional thickness 
given to the rafters in this part of the truss, and more fully 
satisfies the condition of a secondary trapezoidal truss placed 
within a triangular frame to increase its strength. There 



strength. 

are various other modifications of this truss, but the method 
of determining the strains is not affected by them. 



STRAINS ON IRON ROOF-TRUSSES. 



537. The trussing already explained under the head of 
Bridges enters largely into iron roof-trusses. One of the 
most common forms is the one in which the rafters are 
trussed. 




Fig. 210. 



Roof-truss "with trussed rafters. — A common method 
of supporting the middle point of a rafter is shown in Fig. 
210. In this case the lower end of the strut, instead of 
abutting against a king-post, is held up by tie-rods joining it 
with the ends of the rafters. 



roofs. 399 

It is seen from the figure that each rafter, with the strut 
and tie-rod, forms a simple king-post truss inverted. The 
tie-rod connecting the points, E and F, completes the truss. 
This tie-rod sustains the horizontal thrust produced by the 
strains on the rafters, preventing its action on the walls at the 
points of support, B and C. 

In this truss the rafters are equal in length, and make 
equal angles with the horizon ; the struts are placed at the 
middle points and perpendicular to the rafter ; and the 
strains are produced by a uniform load resting on the 
rafters. 

Use the notation of the previous cases, and denote by a 
the angle ABC; by ft, the angle D B E ; by 2b, B C ; by d, 
the height A H ; and by d\ the distance A K. The truss is 
symmetrical with respect to a vertical A H. through the vertex, 
A. Suppose the truss cut in two along this line, A H, we may 
preserve the equilibrium, upon removing the right half, by 
substituting two horizontal forces, one at A and the other at K. 
Suppose this done, and represent these by PI and T respec- 
tively. As the weight of the tie-rods and struts is small 
compared with the load on the rafters, we may neglect it with- 
out material error. 

The reaction at B is equal to wl. 

The external forces acting on the left half of the frame are 
the reaction at B, the horizontal forces H and T at A and K, 
and the load on the rafter including its own weight. These 
forces act in the same vertical plane. 

The analytical conditions for equilibrium are 

H — T = 0, and wl-wl= 0, 
and the bending moment at B is 

wl x B L — H x A K = 0. 

We lind the value of H = \ 

a 

The external forces are now all known and the strains pro- 
duced by them may be determined. 

Pressure on the struts. — Considering the rafter as a 
single beam, there results 

P x = f wl cos a, 

for the pressure on either strut. 

Tension on the tie-rods of the rafters. — Let T 1 be the 

tension on the tie-rod B E, and T 2 the tension on A E. 



400 CIVIL ENGINEERING-. 

At the point, B, the normal pressure must be equal to the 
normal component of the resultant of the forces, wl and T x 
acting at that point, which may be expressed as follows : 

j W wl cos a — wl cos a — T x sin /?, 

and at A, for the same reason, we have 

■f^wl cos a = H sin a — T 2 sin f3. 

These equations give, since H is known, 

Tl = x| W ^ £ an d T 2 = H 8in a ~ y 00S A (169) 

1 b sin j3 sin /3 - J 

for the tensions on the tie-rods B E and A E. 

Tension on the main tie-rod, EF, of the truss.— 

From the analytical condition, 

H — T = 0, 

there results, 

T = H=t*^p., . . (170) 

This may be verified. The strains, P x , T 1? and T 2 , on the 
pieces connected at E (Fig. 210) have been determined. 
These forces with T must be in equilibrium at E. Let us 
find the components of these forces in the direction of the 
strut, D E, and a perpendicular to the strut at E. (Fig. 211.) 

For equilibrium, we have the fol- 
lowing : 

(T x + T 8 ) sin/3 - T sin a - P x = 0, 
and 

(T 2 - T x ) cos£ + T cos a ^ 0. 

\ f t Substituting in the first of these 
pf ^ equations, the values of P l7 T l5 and T 2 , 

Fig 211. already obtained, there results, 

\\ wl cos a -f II sin a — %wl cos a — T sin a — 0, or II = T. 

In a similar manner, by substitution in the 2d, it can be 
shown that the condition is satisfied, or II = T. 

Compression on the rafters. — The compression on the 
rafter at B is due to the components of the forces acting at 
that point parallel to the rafter. Hence 

Compression at B — wl sin a -f T x cos /3, 




ROOFS. 



401 



and 



Compression at A = II cos a + T 2 cos /3. (171) 



Frequently in the construction of this truss, the struts are 
extended until they meet the tie-rod joining B and C. (Fig. 
212.) 




Fig. 212. 

In this case the strains are the same as those just deter- 
mined on the struts and rafters, but less for the secondary 
tie-rods, because of the increase in the angle ft 

538. When the span is considerable, this method of truss- 
ing is oftentimes used to increase the number of supports for 
the rafter. By adding to the trussed rafter, the two struts, 
bf and cd (Fig. 213), and the two secondary tie-rods, /D and 
d D, two additional points of support are furnished to the 
rafter. 




Fig. 213. 



The points, b and c, are midway between B D and A D, divid- 
ing the rafter into four equal parts, and making the triangles 
By'D and D d A equal to each other and similar to B E A. 

Using the previous notation, the reaction at B is wl, and the 

i if a • i w & cos a 

horizontal iorce at A is f j t — , as m previous case. Ihe 

external forces are all known. 

Pressure on the struts.— The struts are respectively per- 
pendicular to the rafter; the normal components of the 
forces acting at b, D, and c will give the amount of pressure 
on each strut, due to the load acting at these points. Repre- 
sent this component at D by P 1? at b and c by P 2 , and at A 
26 



402 CIVIL ENGINEERING. 

and B by P s . Since the rafter is kept by the struts in such a 
position that h, D, and c are in the same straight line with A 
and B, it is an example of a beam resting on live supports, and 
we have, 

P 3 — yW^ cos a i ^2 = \u& cos a ? an d Pi = if^ cos a - 

This value of P 2 is the amount of pressure acting on either 
of the stmts, bfor cd, and the strain on them is determined. 
That on D E is still to be determined. 

Tension on the secondary tie-rods. — Let T x be the ten- 
sion on the rod, B/ and we have, 

ttV w l cos a = wl cos a — T x sin ft, 
from which we get 

113 sin ft 

And in the same way we find the tension T\ on Ad to be 

_ T _. H sin a _ cos a 

sin p * x ^ sin p 

Denote by T 2 , T 3 , T' a , and T' 3 the tensions on/D,/E, d D, 
and dE respectively. Since an equilibrium exists between 
the forces acting at the point f, and the same at d, the com- 
ponents of these forces, taken respectively parallel and per- 
pendicular to the rafter, must fulfil the following conditions : 

T 2 + T 3 - T t = 0, and (T 3 - % - TJ sin ft + P 2 = 0, at/, 

and 

T' a + T' 8 - T\ = 0, and (T' 8 - T' a - T\) sin £ + P 2 = 0, at & 

The values of T 1? P 2 , and T\, have already been found. 
The values for the others are easily deduced. They will be 
as follows : 

P 9 , cos a 



T T" — —— - — i9/j7 



2 sin ft t sin ft' 

T s = T %%wl ^4, and T' s = -=— ; 5 (II sin a - J&wl cos a). 
112 snip sin p v lia l 

Tlie strains of tension and compression on all the secondary 
pieces have been obtained excepting for the strut, D E, at the 
middle. This can now be determined. 



ROOFS. 



403 



Strain on strut, D E, at the middle. — This strain is due 
to the pressure, P t , and the components of T 2 and T' 2 in the 
direction of the strut, or 

Compression on D E = P = P A + (T 2 4- T' 2 ) sin /3. 

Substituting in this for T 2 , T' 2 , and P 1? their values already 
found, we finally obtain, 

P = f^wl cos a, 

for the strain on the strut, D E. 

The amount and kind of strain on each piece are now 
known, and the strength of the truss may therefore be deter- 
mined. 

539. Roof-truss in which the rafters are divided into 
three segments and supported at the points of division by 
struts abutting against a king or queen-posts. 

This form of truss shown in Fig. 214 is in common use for 
roofs. In this case, the rafters are trisected respectively at 
the points, H, D, G, and M, by the struts H K, D F, G F, and 




L F K 

Fig. 214. 



M L, which have their lower ends connected with and abutting 
against the vertical rods at fhe points K, F, and L, where these 
rods are fastened to the tie-rod B C. 

The usual method of determining the amount of strains on 
the different parts of a frame of this kind is to consider it as 
formed of several triangular ones. In this particular case, 
we consider the truss A B C as made up of the secondary 
trusses, B H K, B D F, and B F A, on the right of A F, and 
a similar set on the left of it. 

The strains are supposed to arise from a uniform load over 
the rafters, the weight of the vertical ties and the struts bein^ 
neglected, as in the previous cases. 

In the previous examples, the rafters have been regarded 
as single beams resting on two, three, five, etc., points of sup- 
port, and the reactions of these points of support have been 
taken as the value of the load resting upon them. This pro- 
cess may be followed in this case and is to be preferred, 
whenever the rafters, A B and A C, are continuous. 



404 CIVIL ENGINEERING. 

In most treatises on roofs, the action of the load on the 
points of support are considered in a different manner. There 
are two general methods. Taking either half of a truss 
of this kind, one method is to suppose that each segment 
of the rafter supports one-third of the entire load on the 
rafter ; each segment becomes then the case of a beam sup- 
ported at its ends and uniformly loaded. According to» this 
hypothesis, since \wl is the load on a segment, \wl will 
act at the points, H and D, and \wl^ at B and A, of the half 
A B F. 

The other method is to assume the pressures exerted at the 
four points of support equal to each other, that is, \wl to be 
the load acting at each of the points, B, H, D, and A. This is 
sometimes called " the method of equal distribution of the 
load." 

Adopting the first method, or one-third of the load on the 
rafter resting on each segment, let us first determine the 
strains in the secondary truss, B H K, under this hypothesis. 

Strains onBHK. — By hypothesis, the pressure at H is ^wl, 
which acts vertically downwards. This then is a case of a 
simple triangular frame sustaining a load at the vertex. 

Denote by a, the angle H B K ; since the triangle is isos- 
celes, the components of ^wl along the rafter and strut are 

equal each to I- — , and exert strains of compression in 
^ b sina l 

H B and H K. 

The strain transmitted to B produces a vertical pressure on 
the point of support equal to \wl and a strain of tension in 
B K equal to \wl cot a. 

In like manner, the strain transmitted to K produces at that 
point a vertical pull equal to \iol, which is sustained by the 
tie-rod, D K, and a horizontal strain equal to and directly op 
posed to the strain of tension at B. 

Strains on B D F. — This is also a case of the simple trian- 
gular frame, sustaining a weight at the vertex. 

The load acting at D is ^wl, increased by the pull on the 
tie- rod, D K, or £wl, which is supported by the rafter B D and 
the strut D F. Since these pieces do not make equal angles 
with the vertical through D, the components of &vl in the 
directions of these pieces are not equal. Resolving, we 

on] 

find the one in the direction of the rafter will be 4- , and 

°sm a 

wl 

the other along the strut, -}-. — tt- ; /3 being the angle D F K. 



ROOFS. 405 

The first of these is transmitted to B, where it produces a 
vertical pressure equal to -J W, and a strain of tension on the 
tie-beam equal to \iol cot a. 

The other, transmitted to F, produces a pull on the king- 
post equal to %wl, and a strain of tension on the tie-beam equal 
to and directly opposed to that just found at B, produced by 
the component along the rafter. 

Strains on B F A. — The pressure at A is due to the assumed 
load, \wl and the transmitted load along the king-post, iwl, 
or \wl. 

Resolving this into the components along the rafter A B 

wl 
and a horizontal at A, we have for the first, h- , and 

' sin a ' 

for the latter, \wl cot a. 

The former transmitted to B, produces a vertical pressure 
equal to %wl, and a strain of tension on the tie-beam equal to 
\wl cot <z. 

The horizontal component at A is balanced by an equal and 
directly opposite component for the half A C F. 

Strains on the whole truss. — Knowing the strains in one 
half, and the truss being symmetrical about the vertical 
through A, the strains on all the parts can now be determined. 
Summing and recapitulating, they are as follows: 

^ ^ . . ^ » a « wl * wl , wl e wl 

On B H = C M = h-. hi- ht~ =l~ ' compressive, 

sin a °sin a sin a D sin a L 

wl , wl J wl 
« HD=MG=^ +fc— 



« D A = G A = f - 



sm a sm a "sin a 
wl 



sm a 



wl wl 

" H K = M L = £- > and on D F = G F = f — - Q , " 

b sin a b sm/3 

" DK = GL= -J-wZ, and on A F = ^wl + \wl = ±wl, tensile, 
" BK = CL = \wl cot a, and on K F = F L = fwl cot a, " 

By the use of moments. — These same values may be ob- 
tained by using the principle of moments. To apply this 
principle in determining the strains on the rafter, suppose the 
rafter cut in two by a vertical section on the left of and con- 
secutive to A. The two parts of the truss would tend to ro- 
tate about the point F. Represent the strain of compression 



406 



CIVIL ENGINEERING. 



on the rafter at this section by G v Its direction is parallel to 
A B, and its lever arm, which denote by j?, will be equal to a 
perpendicular let fall from F upon the rafter. The reaction 
at B and the load on the rafter are known. For equilibrium 
we would have, 



Ci x jp = wl x B F — wl x 



B_F 

2 ' 



whence 



C\ = \wl 



db 



b 



We find p to be equal to — , which being substituted in 
this expression gives 

onT? 

.... (172) 






Substituting in (172) the value of d 



/ sin <z, we obtain 



2 sin 



which is the same value already determined. 

If the rafter be cut by a section consecutive to H, we find 

01)7 

the value of (1 to be equal to | -. . 

■ sm a 

540. In the preceding roof -truss, the inclined pieces were 

struts and the verticals were ties. Another form of truss is 

one in which the verticals are struts and the diagonals are 

ties. (Fig. 215.) The rafters are subdivided into' a number 

of equal segments. At each point of division, a strut is 

placed, and kept in a vertical position by the main tie-beam 

and the inclined tie-rods, as shown in the figure. 




Fig. 215. 



The methods previously explained will enable the student 
to determine the kind and amount of strains on each piece of 
the truss. 



ROOFS. 



407 



541. It has been recommended to cheek the accuracy of 
the calculations by some other method than the one used ; 
the graphical method is a very convenient one fortius purpose. 
Let us apply this method to finding the strains in the roof- 
truss referred to in Art. 539. 

The load over the rafters is supposed to act as there taken, 
viz., -J- at A and B, and ^ at H and D, each. 

Assume any point, as 0. From 0, on a vertical line, lay 
off, according to a scale, Ob = \wl, bh — \wl, hd = \wl, 
and da = \wl. These distances represent the loads acting 
at B, H, D, and A, respectively. Their sum Oa — wl, hence, 




Fig. 216. 



aO = — wl represents the reaction at ~, due the load acting 
on the half A B F of the truss. The forces at B are 05, 0«, 
and the stresses upon the pieces B H and B K. Through b, 
draw bf parallel to B H, and through a, draw af parallel to 
B K. ThU polygon aObfa will represent the system of forces 
acting at B, and the lines fa and bf will represent the inten- 
sities of the strains on K B and B H, respectively, at B, and 
may be taken off with the same scale used to lay off the ver- 
tical forces, Ob, bh, etc. 

Going to H, it is seen that the forces acting at this point are 
the weight \wl = bh, the strain bf, and the unknown stresses 
on H K and H D. Through f draw the straight line fj 
parallel to H D. We thus form the polygon, fbhgf which 
will represent the forces acting at H. 

Going to K, the forces' acting to strain B K and H K have 
been determined ; the forces acting in the directions of B K 
and K F are unknown. Through g, draw gk parallel to K D, 
and hit parallel to K F, and we form the polygon, afgka, from 
which the lines gh and ka represent the intensities of the 
strains on D K and K F. 



408 



CIVIL ENGINEERING. 



Iii a similar way, the strains on the other pieces can be 
determined. 

542. Application of graphical method to the roof 
•with trussed ratters.— Let us apply the same method to 
the trussed roof of Art. 537. Instead of the frame being uni- 
formly loaded over the rafters, consider it as supporting a 
load W at the vertex A. (Fig. 217.) 

The applied forces acting on the frame are the load "VV 
and the reactions at B and C. Assume a point, as 0, and lay 
off on a vertical line the distance Ob to represent ~YV. The 
distances be and cO will represent the reactions at B and at 
C. Through b, draw bd parallel to B D, and through c, the 
line cd parallel to B E. The triangle bed will represent the 




Fig. 217. 

4 
system of forces acting at B. Through 0, draw the line 
Gg parallel to cb, and through c, draw the line eg parallel to 
eV. The triangle Oeg will represent the forces acting at C. 

Going to E, since the load on the truss has been supposed 
to act at A, there will be no strain on D E, and the forces at 
E will be those acting in the direction B E already found, and 
the unknown forces along E A and E F. Through d, draw da 
parallel to E A, and through c, draw ca parallel to E F. The 
triangle cda will represent these three forces acting at E. 
And in the same way, the triangle ega would represent the 
strains on the pieces at F. 

If there had been a force acting at E in the direction of 
D E, then there would have been three unknown forces acting 
at E, and we could not have solved the problem until one of 
these were known. 



ROOFS. 409 



PURLINS. 



543. The purlins are simply beams, and are considered as 

resting on two or more supports, according to the number 
of frames connected by them. The strains are easily deter- 
mined. 



CONSTRUCTION OF ROOFS. 



544. The most important element of the roof is the frame. 
The same rules given for frames, and the general methods 
described for their construction apply to the construction of 
the roof -truss. 



A2 







JX 



t 



i 



i 



Mi 















b 



roofs. 409 



PURLINS. 



543. The purlins are simply beams, and are considered as 
resting on two or more supports, according to the number 
of frames connected by them. The strains are easily deter- 
mined. 



CONSTRUCTION OF ROOFS. 



544. The most important element of the roof is the frame. 
The same rules given for frames, and the general methods 
described for their construction apply to the construction of 
the roof- truss. 



4:10 CIVIL ENGINEERING. 



PART VIII. 

ORDINARY ROADS AND RAILROADS. 



CHAPTER XXI. 

ROADS. 



545. A road is defined to be an open way or passage for 
travel, forming a communication between two places some 
distance apart. 

A path or track on which a person can travel on foot is 
the first idea of a road. A line, having been marked out or 
" blazed" between two places, is soon beaten into a well-de- 
fined path by the successive travellers passing over it. A per- 
son travelling over a road like this will find nothing but a 
beaten path on the surface of the ground, with few or no 
modifications of its surface, and generally no conveniences 
for crossing the streams or rivers which intersect it. 

As the travel over a road of this kind increases and beasts 
of burden are used for packing the merchandise, baggage, 
etc., which are to be carried over the route, modifications 
and improvements of the path become necessary. For con- 
venient passage of the animals, the path must be widened, 
the brush and undergrowth removed, temporary bridges con- 
structed or means of ferriage provided for crossing streams 
of any considerable depth, and steep ascents and descents 
be modified and rendered practicable for the pack-animals. 
The term "trail" is used to designate the original path and 
the path improved so that it can be used by pack-animals. 

Since transportation on wheels is cheaper and more rapid 
than by pack-animals, the next step will be to still further 
improve the road so that vehicles on wheels can be used over 
the route. This necessitates a still further widening of the 
trail, a further reduction of the slopes so as to render them 
practicable for carts and wagons, the providing of means to 



ROADS. 41 1 

cross the streams where they cannot be forded, and raising 
the ground in those localities where it is liable to be over- 
flowed. In this condition, the trail is called a road. 

As the travel over this kind of road increases, the want- <! 
conveniences of the community demand a further improve- 
ment of the road so that the time taken in going over it and 
the cost of transportation shall be reduced. This is effected 
by shortening the road where it can be done, reducing still 
further the ascents and descents or avoiding them, and by 
improving the surface of the road. 

It has been proved that a horse can draw up a slope of fa 
only one-half the load he can draw on a level. Hence, a road 
free from these ascents would enable one horse to do the 
work required of two on a road with these slopes. 

It has been shown that a horse can draw over a smooth, 
hard road, as one of broken stone, from three to four times 
as much as he can draw on a soft earthen road. It therefore 
follows that an improvement of the surface will be accom- 
panied by a reduction both in time and cost of the transpor- 
tation. 

546, The engineer may be required to lay out and make a 
road practicable for wagons connecting two settlements or 
points, in a wild, uninhabited, and therefore unmapped conn- 
try, as is the case frequently on our frontier, or he may be 
required to plan and construct a road having for its objects 
the reduction of time and expense incurred in passing over 
it, in a country of which he has maps and other authentic 
information In either case, the general principles guiding 
the engineer are the same. These may be considered under 
the following heads : 1st, Direction ; 2d, Gradients ; 3d, 
Cross-Section ; 4th, Road-Coverings ; 5th, Location ; 6th, 
Construction. 



DIRECTION. 

547. Other things being equal, the shortest line between 
the two points is the one to be adopted, since it costs less to 
construct a short road than a long one ; costs less to keep it 
in repair ; and takes less time and labor to travel over it. 

But straightness will be found of less consequence than 
easv ascents and descents, and as a rule must be sacrificed to 
obtain a level or to make a road less steep. 

Good roads wind around hills instead of running over 
them, and this they may often be made to do without increasing 
their lengths. But even if the curved road, which is prac- 



412 CIVIL ENGINEERING. 

tically level, should be longer, it is better to adopt it ; for 
on it a horse will draw a full load at his usual rate of speed, 
while on the road over the hill, the load most be diminished 
or the horse must reduce his rate of speed. 

Roads are often deviated from the straight line for reasons 
of economy in construction, such as to avoid swampy, marshy, 
or bad ground, or to avoid large excavations, or to reach 
points on streams better suited for the approaches of bridges, 
etc. 

Great care must be exercised in deciding on the line which 
the road is to follow. If the line is badly chosen, the ex- 
pense of construction and repair may be so great that it may 
finally be necessary to change the line and adopt a new one. 

548. The considerations which should govern the selec- 
tion of the line are : to connect the termini by the most 
direct and shortest line ; to avoid unnecessary ascents and 
descents ; to select the position of the road so that its longi- 
tudinal slopes shall be kept within given limits ; and to so 
locate the line that the cost of the embankments, excavations, 
bridges, etc., shall be a minimum. 

The wants of the community in the neighborhood of the 
line oftentimes affect the direction of the line, since it may 
be advisable and even more economical in the end to change 
the direction and pass through important points which do 
not lie on the general direction of the road than to leave 
them off the road. 

GRADIENTS. 

549. Theoretically, every road should be level. If they 
are not, a large amount of the horse's strength is expended in 
raising the load he draws up the ascent. Experiment has 
shown that a horse can draw up an ascent of y-J-^, only 90 
per cent, of the maximum load he can draw on a level ; up 
an ascent of ^ he can draw about 80 per cent. ; of ^ he 
can draw only 64 per cent. ; of 7 1 T , only 50 per cent. ; and of 
- 1 1 ¥ , only 25 per cent. 

These numbers are affected by the nature and condition of 
the road, being different for a rough and for a smooth road, 
the resistance of gravity being more severely felt on the 
latter. 

A level road is therefore the most desirable, but can seldom 
be obtained. The question is to select the maximum slope 
or steepest ascent allowable. 

As an ascent, it chiefly affects the draught of heavy loads, 
as has been already shown. 



GRADIENTS. 413 

As a descent, it chiefly concerns the safety of rapid travel- 
ling. 

550. The slope or grade of a road depends upon the kind 
of vehicle used, the character of the road-covering, and the 
condition in which the road is kept. From the experiments 
above mentioned it would seem that the maximum grade for 
ascent should not be greater than 1 in 30, although 1 in 20 
may be used for short distances. 

For descent, the grade should be less than the angle of 
repose, or that inclination in which a vehicle at rest w r ould 
not be set in motion by the force of gravity. This angle 
varies with the hardness and smoothness of the road-covering, 
and is affected by the amount of friction of the axles and 
wheels of the vehicles. On the best broken stone roads in 
good order, using ordinary vehicles, the maximum grade is 
taken at 1 in 35. 

Steeper grades than these named produce a waste of ani- 
mal power in ascending and create a certain amount of dan- 
ger in descending. * 

551. Although theoretically the road should be level, in 
practice it is not desirable that it should be so, on account of 
the difficulty arising of keeping the surface free from water. A 
minimum inclination is therefore to be selected, below which 
ir, is not desirable to have the surface of the road. This slope 
is taken at 1 in 125, and in a level country it is recom- 
mended to form the road by artificial means into gentle un- 
dulations approximating to this minimum. 

It is generally thought that a gentle undulating road is less 
fatiguing to a horse than one which is level. Writers who 
hold this opinion attempted to explain it by reference to the 
muscles of the horse, stating that as one set is brought into 
play during the ascent and another during the descent, that 
some of the muscles are allowed to rest, while others, those in 
motion, are at work. This explanation has no foundation in 
fact, and is therefore to be rejected. The principal advan- 
tage of an undulating road is not the rest it gives the horse, 
but the facilities which are afforded to allow the water to flow 
off the surface of the road. 

CROSS- SECTION. 

552. The proper width and form of roadway depend upon 
the amount and importance of the travel over the road. 

Width. — The least width to enable two vehicles to pa?s 
with ease is assumed at 16-J feet. The width in most of the 
States is fixed by law\ 



414 CIVIL ENGINEERING. 

In England, the width of turnpike roads approaching 
large towns, on which there is a great amount of travel, is 
60 feet. Ordinary turnpike roads are made 35 feet wide. Or- 
dinary carriage roads across the country are given a width 
of 25 feet ; for horse-roads, the width is 8 feet ; and for foot- 
paths, 6-J feet. 

Telford's Holyhead road is made 32 feet wide on level 
ground ; 28 feet wide in moderate excavations ; and 22 feet 
in deep excavations and along precipices. 

In France there are four classes of main roads. The first 
or most important are made 66 feet wide, the middle third of 
which is paved or made of broken stone. The second class 
are 52 feet wide ; the third are 33 feet wide ; and the fourth 
are 26 feet wide. All these have the middle portion ballasted 
with broken stone. 

The Eoman military roads had their width established by 
law, at twelve feet when straight and sixteen when crooked. 

Where a road ascends a hill by zigzags it should be made 
wider on the curves connecting the straight portions ; this in- 
crease of width being one-fourth when the angle included 
between the straight portions is between 120° and 90°, and 
one-half when the angle is between 90° and 60°. 

553. Form of roadway. — The surface of the road must 
not be flat, but must be higher at the middle than at the 
sides, to allow the surface water to run off freely. 

If the surface is made flat, it soon becomes concave from 
the w r ear of the travel over it, and forms a receptacle for 
water, making a puddle if on level ground, and a gulley if 
the ground is inclined. 

The usual shape given the cross-section of the roadway 
is that of a convex curve, approaching in form a segment of 
a circle or an ellipse. This form is considered objectionable 
for the reasons that water stands on the middle of the road ; 
w r ashes away its sides ; that the road wears unequally, and 
is very apt to wear in holes and ruts in the middle ; and that 
when vehicles are obliged to cross the road, they have to 
ascend a considerable slope. 

554. The best form of the upper surface of the roadway is 
that of two inclined planes rounded off at their intersection 
by a curved surface. The section of this curved surface is a 
flat segment of a circle about live feet in length. 

The inclination of the planes will be greatest where the 
surface of the road is rough and least where it is smoothest 
and hardest. A slope of ^ is given a road with a broken 
stone covering, and may be as slight as ,-'„ for a road paved 
with square blocks. The transverse slope should always 



DITCHES. 41 5 

exceed the slope of the road in the direction of its length, 
so as to prevent the surface water from running too far in 
the direction of the road. 

On a steep hillside, the surface of the roadway should be 
a plane inclined inwards to the face of the hill. A ditch on 
the side of the road next to the hill receives the surface 
water. ** 

555. Foot-paths. — On each side of the roadway, foot-paths 
for the convenience of passengers on foot should be made. 
They should be from five to six feet wide and be raised about 
six inches above the roadway. The upper surface should 
have an inclination towards the " side channels," to allow the 
water to flow into them and thence into the ditches. When 
the natural soil is firm and sandy, or gravelly, its surface will 
seiwe for the foot-paths ; but if loam or clay, the soil should 
be removed for six inches and the excavation filled with 
gravel. 

Sods, eight inches wide and six inches thick, should be 
laid against the side slope of the foot-path next to the road, to 
prevent the wash from the water running in the side chan- 
nels. 

Fences, hedges, etc., where the road is to be enclosed, 
should be placed on the outside of the foot-paths, and outside 
of these should be the ditches. (Fig. 218.) 




Fig. 218. — a, cross-section of roadway; 5, 6, foot-paths ; /, /, fences; 
d, d, ditches ; s, s, side drains. 

556. Ditches. — Ditches form an important element in the 
construction of a good road. 

The surface of the road has been given a form by means 
of which the water falling on it is carried off into the gut- 
ters or side channels of the road, whence it is conveyed by 
side drains, s, s (Fig. 218), into ditches, which immediately 
carry off all the water which enter them. 

The ditches are s*unk to a depth of about three feet below 
the roadway, so that they shall thoroughly drain off the 
water which may pass through the surface of the roadway. 
These ditches should lead to the natural water- courses of the 
country, and have a slope corresponding to the minimum lon- 
gitudinal slope of the road. Their size will depend upon 
circumstances, being greater where they are required to carry 



416 CIVIL ENGINEERING. 

away the water from side-hills or where they are made in 
wet grounds. A width of one foot at the bottom will gen- 
erally be sufficient. 

There should be a ditch on each side of the road, on level 
ground or in cuttings. One is sufficient where the road is on 
the side of a hill. 

557. Side-slopes. — The side-slopes^ of the cuttings and 
embankments on each side of the road vary with the nature 
of the soil. 

Rock cuttings may be left vertical or nearly so. Common 
earth should have a slope of at least f, and sand, -J-. Clay is 
treacherous and takes different slopes according to its liabil- 
ity to slip and the presence of water. The slope to give it, 
as well as the others, is best determined by observing the 
slope assumed by these earths in the locality of the wx>rk 
where exposed to the weather. 

When the road is in a deep cutting, the side slopes should 
not be steeper than J, so as to allow the road, by its exposure 
to the sun and wind, to be kept dry. 

Whenever the side-slopes are of made earth, earth removed 
and placed in position like that of an enbankment, the slopes 
should be more gentle. 

ROAD-COVERINGS. 

558. The road-covering of a common country road, and 
most generally of all the new roads in our country, is the 
natural soil thrown on the road from the ditches on each side. 
In many cases there are even no ditches, and the road-cover- 
ing or upper surface of the roadway is the natural soil as it 
exists on the hard subsoil beneath, which is exposed when the 
soft material has been removed by scraping or by some other 
method. 

Roads of this kind are deficient in the qualities of hard- 
ness and softness. To improve these roads, it is necessary to 
cover the surface with some material, as wood, stone, etc., 
which will substitute a hard and smooth surface for the soft 
and uneven earth, and which, acting as a covering, will pro- 
tect the ground beneath from the action of the water that 
may fall upon it. 

559. Roads may be classified from their coverings as 
follows : 

I. Earth roads. 

II. RoADS OK WOOD. 

III. Gravel roads. 

IV. Roads ok broken stone. 






CORDUROY ROADS. 417 

Y. Ro ADS PAVED WITH STONE. 

VI. EOADS COVERED OR PAVED WITH OTHER MATERIALS. 

VII. Tram-roads. 



I. EARTH ROADS. 

560. These are the most common and almost the only kind 
of roads in this- country. From what has been said, we know 
that they are deficient in hardness and generally in smooth- 
ness. In wet weather, when there is much travel of a heavy 
kind over them, they become almost impassable. 

The principal means of improvement for these roads are to 
reduce the grades, thoroughly drain the roadway, and freely 
expose the roadway to the influence of the sun and wind. In 
repairing them, the earth used to fill the holes and hollows 
should be as gravelly as possible and free from muck or 
mould. Stones of considerable size should not be used, as 
they are liable to produce lumps and ridges, making an un- 
even surface disagreeable to travel upon. 



II. ROADS OF WOOD. 

I 561. Corduroy roads. — When a road passes over a marsh 
or soft swampy piece of ground which cannot be drained, or 
the expense of which would be too great, a corduroy road 
is frequently used. This kind of road is made by laying 
straight logs of timber, either round or split, cut to suitable 
lengths, side by side across the road at right angles to its 
length. 

It is hardly worthy of the name of a road, and is extremely 
unpleasant to persons riding over it, but it is nevertheless 
extremely valuable, as without it, the swamp across which it 
is laid would at times be impassable. 

562. Plank roads. — In districts where lumber is cheap 
and gravel and stone cannot be easily obtained, road-coverings 
of plank have been used. 

The method most generally adopted in constructing a road 
of this class consists in laying a flooring or track, eight feet 
wide, of boards from nine to twelve inches in width and 
three inches in thickness, which rest upon two parallel rows 
of sleepers, or sills, laid lengthwise of the road, and having 
their centre lines about four feet apart, or two feet from the 
axis of the road. 

The boards are laid perpendicular to the axis of the road, 
27 



418 CIVIL ENGINEERING. 

experience having shown that this position is as favorable to 
their durability as any other, and is the most economical. 

When the rroad is new and well made it offers all the ad- 
vantages of a good road and is a very pleasant one to use. 
But when the planks become worn and displaced it makes a 
very disagreeable and indifferent road. 

Some years ago they were much used, but as a general 
thing they are no longer built except under very peculiar 
and urgent circumstances. 

III. GRAVEL ROADS. 

563. These are roads upon which a covering of good gravel 
has been laid. 

The roadway is first prepared by removing the upper layer 
of soft and loose earth, and thoroughly draining the road. 
The bed is sometimes of the shape of the upper surface of the 
road, but more generally it is merely made level ; on this a 
layer of gravel about four inches in thickness is laid, and 
when compacted by the travel over it another layer is laid, 
and so on until a thickness of sixteen inches at the centre 
has been reached. 

It is advisable to compress the bed by rolling it well with 
a heavy iron roller before beginning to lay the gravel. In 
some cases a bed of broken stone has been used. $ 

Gravel from the river shores is generally too clean for this 
kind of road, there not being enough clayey material mixed 
with it to bind the grains together. On the other hand, 
gravel from pits is apt to be too dirty and requires a partial 
cleansing to fit it for this purpose. 

The gravel used should be sifted through screens, and all 
pebbles exceeding two inches in diameter be broken into 
small pieces or rejected. 

The iron roller can be advantageously used to assist in 
compacting the layers of gravel as they are put on the road. 

A gravel road carefully made, with good side ditches to 
thoroughly drain the road-bed, forms an excellent road. 

Some gravel roads are very poor, even inferior to an earth 
road, caused in a great measure by using dirty gravel which 
is carelessly thrown on the road in spots, which cause the road 
to soon wear into deep ruts and hard ridges. 

IV. ROADS OF BROKEN STONE. 

5G4. The covering of roads of this class, both in this 
country and Europe, is composed of stone broken into small 



■TELFOED EOADS. 



419 



angular fragments. These fragments are placed on the natu- 
ral bed in layers, as in the gravel road, or they may be placed 
in layers on a rough pavement of irregular blocks of stone. 

505. Macadamized roads. — When the stone is placed on 
the natural road-bed, the roads are said to be " macadamized," 
a name derived from Mr. McAdam, who iirst brought this 
kind of road into general use in England. 

The construction of this road is very similar to that just 
given for a gravel road. The roadway having received its 
proper shape and having been thoroughly drained, is covered 
with a layer of broken stones from three to four inches thick. 
This layer is then thoroughly compacted by allowing the 
travel to go over it and by rolling it also with heavy iron 
rollers ; care being taken to fill all the ruts, hollows, or other 
inequalities of the surface as fast as they are formed. Suc- 
cessive layers of broken stone are then spread over the road 
and treated in the same manner, until a thickness of between 
eight and twelve inches of stone is obtained. Care is taken 
that the layers, when they are spread over the surface, are 
not too thick, as it will be difficult, even if it be possible, to 
get the stone into that compact condition so necessary for a 
good road of this kind. 

566. Telford roads. — This is the name given to the broken 
stone roads in which the stone rests on a rough pavemfent 
pi^pared for the bed. (Fig. 219.) 




Fig. 219. 



This pavement is formed of blocks of stone of an irregular 
pyramidal shape ; the base of each block being not more 
than five inches, and the top not less than four inches. 

The blocks are set by the hand as closely in contact at their 
bases as practicable ; and blocks of a suitable size are selected 
to give the surface of the pavement a slightly convex shape 
from the centre outwards. The spaces between the blocks 
are filled with drippings of stone compactly set with a small 
hammer. 

A layer of broken stone, four inches thick, is then laid 
over this pavement, for a width of nine feet on each side of 
the centre ; no fragment of this layer should measure over 



420 CIVIL ENGINEERING 

two and a half inches in an}' direction. A layer of broken 
stone of smaller dimensions, or of clean coarse gravel, is 
spread over the wings to the same depth as the centre layer. 

The road- covering, thus prepared, is thrown open to travel 
until the upper layer has become perfectly compact ; care 
having been taken to fill in the ruts as fast as formed with 
fresh stone, in order to obtain a uniform surface. A second 
layer, about two inches in depth, is then laid over the centre 
of the roadway ; and the wings receive also a layer of new 
material laid on to a sufficient thickness to make the outside 
of the roadway nine inches lower than the centre. A coat- 
ing of clean coarse gravel, one inch and a half thick, is then 
spread over the surface, and the road-covering is considered 
as finished. 

The stone used for the pavement may be of an inferior 
quality in hardness and strength to the broken stone on top, 
as it is but little exposed to the wear and tear occasioned by 
travelling. The surface-stone should be of the hardest kind 
that can be procured. 

567. Kind of stone used for broken stone roads. — The 
stone used for these roads should be selected from those 
which absorb the least water, and are also hard and not brit- 
tle. All the hornblende rocks, porphyry, compact feldspar, 
andf some of the conglomerates furnish good, durable road- 
coverings. Granite, gneiss, limestone, and common sand- 
stones are inferior in this respect, and are used only when tne 
others cannot be obtained. 

568. Repairs. — Broken stone roads to be good must be 
kept in thorough repair. If the road is kept in order it will 
need no repairs. The difference between " kept in order " 
and " repairs " is that the latter is an occasional thing, while 
the former is a daily operation. To keep the road in order 
requires that the mud and dust be daily removed from the 
surface of the road and that all ruts, depressions, etc., be at 
once filled with broken stone. 

It is recommended by some that when fresh material is 
added, the surface on which it is spread should be broken 
with a pick to the depth of half an inch to an inch, and the 
fresh material be well settled by ramming, a small quantity 
of clean sand being added to make the stone pack better. 
When not daily repaired by persons whose sole business it is to 
keep the road in good order, general repairs should be made 
in the spring and autumn by removing all accumulations of 
mud, cleaning out the side channels and other drains, and 
adding fresh material where requisite. 

If practicable, the road-surface at all times should be kept 



SOMAN ROADS. 421 

free from an accumulation of mud and dust, and the surface 
preserved in a uniform state of evenness by the daily addition 
of fresh material wherever the wear is sufficient to call for it. 
Without this constant supervision, the best constructed road 
will, in a short time, be unfit for travel, and with it the weak- 
est may at all times be kept in a tolerably fair condition. 



V. ROADS PAYED WITH STONE. 

569. A good pavement should offer but little resistance to 
the wheels, and at the same time give a firm foothold to 
horses ; it should be durable, free from noise and dirt, and 
so constructed as to allow of its easy removal and replace- 
ment whenever it may be necessary to gain access to gas or 
water pipes which may be beneath it. 

570. Roman roads. — The ancient paved Roman roads, 
traces of which may still be seen as perfect as when first 
made, were essentially dressed stone pavements with concrete 
foundations resting on sub-pavements. The entire thickness 
of the road-covering was about three feet, and was made as 
follows : 

The direction of the road was marked out by two parallel 
furrows in the ground, and the loose earth from the space 
between them removed. A bed of mortar was then spread 
over the earth, and on this the foundation (statumen), com- 
posed of one or two courses of large flat stones in mortar, 
was laid. On this foundation was placed a course of con- 
crete (rudus), composed of broken stones. If the stones 
were freshly broken, three parts of stone to one of lime were 
used ; if the stone came from old buildings, two parts of lime 
were used. On this course a third (nucleus), composed of 
broken bricks, tiles, pottery, mixed with mortar, was placed. 
In this layer was imbedded the large blocks of stone (sum- 
ma crusta) forming the pavement. These stones were ir- 
regular in form, rough on their under side, smooth on their 
upper, and laid so that the upper surface should be level. 
They were laid with great care and so fitted to each other as 
to render the joints almost imperceptible. 

When the road passed over marshy ground, the foundation 
was supported by timber-work, generally of oak ; the timber 
was covered with rushes, reeds, and sometimes straw, to pro- 
tect it from contact with the mortar. 

On each side of the roadway were paved foot-paths. 

571. English paved roads. — Some of the paved roads in 
England are partial imitations of the Roman road. This 



422 CIVIL ENGINEERING. 

pavement (Fig. 220) was constructed by removing the sur- 
face of the soil to the depth of a foot or more to obtain a firm 
bed. If the soil was soft it was dug deeper and a bed of 
sand or gravel made in the excavation. On this a broken 
stone road-covering similar to those already described was 
laid. On this broken stone was spread a layer of fine clean 




Fig. 220. 

gravel, two and a half inches thick, on which rest the paving 
stones. The paving stones are of a square shape, and are of 
different sizes, according to the nature of the travel over 
the road. The largest size are ten inches thick, nine inches 
broad, and twelve inches long ; the smallest are six inches thick, 
five inches broad, and ten inches long. Each block was 
carefully settled in its place by means of a heavy rammer ; 
it was then removed in order to cover the side of the one 
against which it rested with hydraulic mortar ; this being 
done, the block was replaced, and properly adjusted. The 
blocks of the different courses across the roadway break 
joints. 

This pavement fulfils all the conditions required of a good 
road-covering, presenting as it does a hard even surface to 
the action of the wheels, and reposing on a firm bed formed 
by the broken-stone bottoming. The mortar-joints, so long 
as they remain tight, will effectually prevent the penetration 
of water beneath the pavement. 

572. Belgian pavement. — This pavement, so named from 
its common use in Belgium, is made with blocks of rough 
stone of a cubical form measuring between eight and nine 
inches along the edge of the cube. These blocks are laid on 
a bed of sand of only a few inches thick when the soil beneath 
is firm ; but in bad soils the thickness is increased to from 
six to twelve inches. The transversal joints are usually con- 
tinuous, and those in the direction of the axis of the road 
break joints. In some cases the blocks are so laid that the 
joints make an angle of 45° with the axis of the roadwa} r , 
one set being continuous, the other breaking joints with them. 
By this arrangement of the joints, the wear upon the edges 
of the blocks, by which the upper surface soon assumes a con- 
vex shape, is diminished. It has been ascertained by experi- 
ence, that the wear upon the edges of the block is greatest at 



WOODEN PAVEMENTS. 423 

the joints which run transversely to the axis when the blocks 
are laid in the usual manner. 

When a bed of concrete is used, instead of or in addition 
to a bed of sand, and the upper surface of the blocks is rec- 
tangular instead of square, there results a pavement much 
nsed in New York City. 

573. Cobble-stone pavement. — Rounded pebbles (cobble 
stones) are used frequently for pavements. This pavement 
is composed of round or egg-shape pebbles, from five to ten 
inches long, three to six inches wide, set on end in a bed of 
sand or fine gravel, and firmly settled in place by pounding 
with a heavy rammer. Aiter the stones are driven, the road- 
surface is covered with a layer of clean sand or gravel, two 
or three inches thick. 

The objections to this pavement are its roughness ; its 
resistance offered to the wheels ; the noise ; the ease with 
which the stones are pressed down in the ground by heavy 
loads passing over them, forming holes in the road ; the dif- 
ficulty of cleaning its surface ; and its need of frequent 
repairs. 

574. Kind of stones used for pavements. — The fine-grained 
granites which contain but a small proportion of mica, and the 
fine-grained silicious sand-stones which are free from cla} T , 
form good material for blocks for paving. Mica slate, talcose 
slate, hornblende slate, some varieties of gneiss, and some 
varieties of sand-stone of a slaty structure, yield excellent 
materials for pavements for sidewalks and paths. 



VI. ROADS OF OTHER MATERIALS. 

575. Wooden blocks have been much used recently in 
paving the streets of our towns and cities. Brick, concrete, 
asphalte, and even castiron, are or have been used for road- 
coverings. Roads near blast-furnaces are frequently seen 
covered with the slag from the furnaces, and those near kilns 
where cement is burned, with cinders and clinkers from 
the kilns. Road-coverings of charcoal have been tried in 
Michigan and Wisconsin. 

The wooden, brick, and asphaltic pavements are the most 
common of these. 

576. Wooden pavements. — Wooden pavements are the 
same in principle as stone. The road-bed is formed and 
the blocks of wood are placed in contact with each other upon 
the surface of the road-bed as described for the blocks of 
stone pavements. The wooden blocks are parallelopipedons 



424 CIVIL ENGINEEEING. 

m form and are laid with the grain of the wood in the direc- 
tion of the depth of the road. From slight differences in the 
details of construction of wooden pavements there has arisen 
quite a variety of names, as the Nieolson, the bastard Nicolson, 
the Stowe, the Greeley, the unpatented, etc., all nsing the 
wooden blocks, but differing slightly in other ways. 

Wooden pavements offer a smooth surface ; are easily 
kept clean ; not noisy ; easy for the horses and vehicles ; 
pleasant to ride upon ; and are cheaper at first cost than 
stone pavements. For these reasons they have been much 
used in the United States. 

They are, however, slippery in wet weather; soon wear out ; 
and unfit for roads or streets over which there is a heavy travel. 
True economy forbids their use except as temporary roads. 

577. Asphaltic coverings. — Asphaltic roads may be com- 
posed of broken stone and this covered with asphaltic con- 
crete, or the broken stone covered with ordinary concrete and 
this overlaid with a covering of asphalte mixed with sand. 
Asphaltic roads present a smooth surface which does not 
become slippery by wear ; a surface free from dust and mud ; 
not noisy ; and from its imperviousness to moisture forms 
an excellent covering over the road-bed beneath and prevents 
the escape of noxious vapors from below. 

Asphaltic roads properly made are growing steadily in 
favor and when they are better known will be more generally 
adopted for all streets in towns and cities, over which the 
travel is light. 

VII. TKAM-EOADS. 

In order that the tractive force should be a minimum, the 
resistance offered to the wheels of the carriage should be a 
minimum. In other words, the harder and smoother the 
road, the less will be the tractive force required. But car- 
riages drawn by horses require that the surface of the road 
should be rough, to give a good foothold to the horses' feet. 
These two opposite requirements are united only in roads 
with track- ways, on which there are at least two parallel 
tracks made of some hard and smooth material for the wheels 
to run upon, while the space between the tracks is covered 
with a different material suitable for the horses' feet. Con- 
structions of this class are termed '-tram-roads" or ''tram- 
ways." The surface of the tracks or " trams " are made fiush 
with that of the road and are suitable for the wheels of ordi- 
nary carriages. Their construction will be alluded to in the 
next chapter. 



RECONNOISSANOE. 425 



CHAPTER XXII. 

LOCATION AND CONSTRUCTION OF ROADS. 

578. In establishing a road to afford means of communi- 
cation between two given places, there are several points 
which must be considered by the engineer and those inter- 
ested in its construction. These are the kind of road to be 
selected, the general line of direction to be chosen or located, 
and the construction of the road. 

The selection of the kind of road depends upon the kind 
of travel which is to pass over it ; the amount of travel, both 
present and prospective ; and the wants of the community 
in the neighborhood of the line. The location and construc- 
tion of the road depend upon the natural features of the 
country through which the road must pass, and' as these come 
exclusively within the limits of the engineer's profession, 
they alone will be considered in this chapter. 

LOCATION. 

579. Reconnoissanoe. — The examination and study of the 
country by the eye is termed a reconnoissanoe, and is usually 
made in advance of any instrumental suiweys, to save time 
and expense. The general form of the country and the ap- 
proximate position of the road may frequently be determined' 
by it. 

A careful examination of the general maps of the country,, 
if any exist, will lessen the work of the reconnoissance very 
much, as by this the engineer will be able to discover many 
of the features which will be favorable or otherwise to the 
location of the road in their vicinity. 

Roads along the bank of a large stream will have to cross 
a number of tributaries. Roads joining two important 
streams running nearly parallel to each other must cross high 
ground or dividing ridges between the streams. 

An examination of the map will show the position of the 
streams, and from these the engineer may trace the general 
directions of the ridges, determine the lowest and highest 
points, and obtain the lines of greatest and least slopes.. 



426 



CIVIL ENGINEERING. 



With this information the directions of the roads leading from 
one valley to another may be approximately located. 

It is seen (Fig. 221) that if A and B are to be joined by a 
road, that the road may run direct from A to B, as shown by 
the dotted line joining them, or it may go, by following the 




Fig. 221. 

general directions of the streams,-through C, as shown by the 
dotted line A C B. By the first route, the road would be 
apparently shorter, but the ascents and descents would be 
greater ; by the second, the road , would be longer, but the 
ascents and descents more gentle, and the total difference of 
level to be passed over would be less. 

We can draw this conclusion from the fact that the streams 
have made for themselves channels which follow the lines of 
gentlest slope. And that if two streams flow in the same 
direction, the high ground or ridge separating them has 
the same general direction and inclination as the streams. 
And if two streams approach each other near their sources, 
as those at C in the figure, that this indicates a depression in 
the main ridge in this vicinity. 

Hence long lines of road usually follow the valleys of 
streams, obtaining in this way moderate grades and crossing 
the ridges by the lowest passes. 

The engineer having studied thoroughly the map and made 
himself acquainted with the natural features of the country 
as there indicated, proceeds to make a personal examination 
of the ground, to identify these natural features, and to verify 
the conclusions deduced from the study of the map. 

In making the examination, he goes both forwards and 
backwards over the ground so as to see it from both direc- 



ESTIMATE OF THE COST. 427 

tions, and in this way verify or correct the impressions he has 
received as to its nature. 

By means of the reeonnoissance he establishes "approxi- 
mate" or "trial lines" for examination. These lines are 
marked out by "blazing " if in a wooded country, or by stout 
stakes driven at the important points if the country be a 
cleared or open one. 

580. Surveys. — The surveys are divided into three classes : 
preliminary surveys, surveys of location, and surveys of con- 
struction. 

The preliminary survey is made with ordinary instru- 
ments, generally a transit and a level, and has for its object 
the measurement of the length of the road, the changes of 
direction of the different courses, the relative heights of the 
different points or differences of level along the line, and of 
obtaining the topography of the country passed over in the 
immediate neighborhood of the line. 

The line is run without curves, and therefore, when plot- 
ted, consists of a series of straight lines of different lengths, 
forming at their connection angles of varying size. 

The levelling party, besides taking the measurements re- 
quisite to construct a profile of the line, make cross-section 
levellings at suitable points, so as to show the form of surface 
of the road. 

The topography on each side of the line is ordinarily 
sketched in by eye ; instrumental measurements being occa- 
sionally made to check the work. 

581. Map and memoir. — The results of these survevs 
are mapped, and all the information gathered during the 
survey which cannot be shown on the map is embodied in a 
memoir. 

From these trial lines thus surveyed, the engineer makes a 
selection, being governed by the considerations mentioned in 
Art. 567, viz., shortness of route, avoidance of unnecessary 
ascents and descents, selection of favorable grades, and econ 
omy of construction. 

582. Estimate of the cost. — This can be made ap- 
proximately after the engineer has established the grades. 

The kind of road and the character of the travel over it 
generally fix the limits of its longitudinal slopes. To fix 
them exactly, the engineer constructs the profiles of the dif- 
ferent sections of the road and draws the "grade lines" on 
these profiles, keeping their slopes within the general limit 
already assumed. Thus in a profile (Fig. 222) the grade 
line A B is drawn, following the mean or general slope of the 
ground, equalizing as far as possible the undulations of the 



42S 



CIVIL ENGINEERING. 



profile above and below the grade line. The inclination of 
the grade line with the horizontal is then measured, and if its 
slope falls within the limit assumed, the grade is a satisfactory 
one and the amounts of excavation and embankment are 
nearly equal. If the inclination be found too steep, either 




"20'dd'r 
Fig. 222. 



the top of the hill must be cut down or the length of the line 
between the two points at top and bottom be increased. The 
latter is the method usually adopted. Thus if the road laid 
out on a straight line joining C and D (Fig. 223) requires a 




Fig. 223. 



steeper grade than the maximum grade adopted, the length 
of the road between these points, C and D, may be increased 
by curving it, as shown by the line C E F D. The length to 
give this winding road is easily determined so that the grade 
of every portion of the road shall be kept within the assumed 
limit. The proper grade, line having been determined and 
drawn on the profiles, the height of the embankments and 
the depth of the cuttings are determined. 

Knowing the width of the road, the form of its surface, 
and the inclination of the side slopes, the cubical contents of 
the excavations and embankments may be calculated, and an 
estimate of the cost made. 

The comparative costs of the routes being determined and 
the considerations mentioned in last article given their full 
weight, the engineer selects the particular line for the road. 

It is well to say that it happens often that no trial lines 



SURVEYS. 429 

are necessary ; the route to be followed by the road being 
apparent. 

583. Survey of location. — The route being selected, it is 
gone over again and more accurately surveyed. It is care- 
fully levelled at regular intervals in the direction of its length, 
and cross-levels at all important points are made. The angles 
made by the changes of direction of the line are rounded off 
by curves, the curves being generally arcs of circles. Ad- 
vantage is taken of this survey to place the line in its best 
position so as to reduce to a minimum the embankments 
and excavation, and to give the best approaches to the points 
where streams are to be crossed. 

The line is divided into a number of divisions, and maps of 
these divisions are made showing the road in plan and the 
longitudinal and cross-sections of the natural ground, with 
the horizontal and vertical measurements written upon them. 

By these maps, the engineer can lay out the line on the 
ground and can determine the amount of excavation and 
embankment required for each division. 

Besides these maps, detailed drawings of the road-cove ring, 
of the bridges, culverts, drains, etc., with the written specifi- 
cations explaining how the w T ork on each must be done, should 
be prepared. 

The work is now in the condition that estimates of its cost 
can be accurately made and its construction begun. 

584. Survey of construction, — The road is constructed 
b}' contract or " day labor." Whichever method is adopted, 
it is first necessary to "lay out the work." This laying out 
the work forms the third class of surveys, or survey of con- 
struction. 

From the maps showing the location, the engineer proceeds 
to mark out the axis of the road upon the ground by means 
of stout pegs or stakes driven at equal intervals apart, using a 
transit or theodolite to keep them in the proper line. These 
stakes are numbered to correspond with the same points indi- 
cated on the map. 

The width of the roadway and the lines on the ground 
corresponding to the side slopes of the excavations and em- 
bankments, are laid out in the same manner, by stakes placed 
along the lines of the cross profiles. 

Besides the numbers marked on the stakes, to indicate their 
position on the map, other numbers, showing the depth of the 
excavations, or the height of the embankments from the sur- 
face of the ground, accompanied by the letters Cut. Fill, to 
indicate a cutting, or a filling - , as the case may be, are also 
added to guide the workmen. The positions of the stakes on 



430 CIVIL ENGINEERING. 

the ground, which, show the principal points of the axis of the 
road, should be laid down on the map by bearings and dis- 
tances from bench-marks in their vicinity, in order that the 
points may be readily found should the stakes be subsequently 
misplaced. 

Curves. — Curves are not necessary for common roads, but 
it always looks better even in a common road to join two 
straight portions by a regular curve than by a bent line. 

Curves are laid out by means of offsets from a chord or tan- 
gent, or by angles of deflection from the tangent. The latter 
method, using a transit or theodolite, is the one most com- 
monly employed. 

CONSTRUCTION. 

585. Earth- work. — This term is applied to all that relates 
to the excavations and embankments, whatever be the mate- 
rial excavated or handled. 

Excavations. — In forming the excavations, the inclination 
of the side slopes demands particular attention. This incli- 
nation? will depend on the nature of the soil, and the action of 
the atmosphere and internal moisture upon it. In common 
soils, as ordinary earth formed of a mixture of clay and sand, 
hard clay, and compact stony soils, although the side slopes 
would withstand very well the effects of the weather with 
a greater inclination, it is best to give them a slope of i ; 
as the surface of the roadway will, by this arrangement, be 
better exposed to the action of the sun and air, which will cause 
a rapid evaporation of the moisture on the surface. Pure 
sand and gravel require a slope of -J. In all cases where the 
depth of the excavation is great, the base of the slope should 
be increased. It is not usual to use artificial means to protect 
the surface of the side slopes from the action of the weather ; 
but it is a precaution which, in the end, will save much labor 
and expense in keeping the roadway in good order. The 
simplest means which can be used for this purpose, consist in 
covering the slopes with good sods, or else with a layer of 
mould about four inches thick, and sown with grass-seed. 
These means will be amply sufficient to protect the side 
slopes from injury when they are not exposed to any other 
causes of deterioration than the wash of the rain and the 
action of frost on the ordinary moisture retained by the soil. 

The side slopes form usually an unbroken surface from the 
foot to the top. But in deep excavations, and particularly in 
soils liable to slips, they are sometimes formed with horizontal 
offsets, termed bericlies, which are made a few feet wide and 



EMBANKMENTS. 431 

have a ditch on the inner side to receive the surface-water 
from the portion of the side slope above them. These benches 
catch and retain the earth that may fall from the portion of 
the side slope above. 

In excavations through solid rock, which does not disinte- 
grate on exposure to the atmosphere, the side slopes might be 
made perpendicular; but as this would exclude, in a great 
degree, the action of the sun and air, which is essential to 
keeping the road-surface dry and. in good order, it will be 
necessary to make the side slopes with an inclination, varying 
according to the locality ; the inclination of the slope on the 
south side in northern latitudes being greatest, to expose bet- 
ter the road-surface to the sun's rays. 

Embankments. — In forming the embankments, the side 
slopes should be made less than the natural slope ; for the pur- 
pose of giving them greater durability, and to prevent the width 
of the top surface along which the roadway is made from 
diminishing by every change in the side-slopes, as it would 
were they made with the natural slope. To protect more 
effectually the side-slopes, they should be sodded or sown in 
grass seed; and the surface water of the top should not be 
allowed to run down them, as it would soon wash them into 
gullies and injure the embankment. In localities where 
stone is plenty, a retaining wall of dry stone may be advan- 
tageously substituted for the side-slopes. 

To reduce the settling which takes place in embankments, 
the earth should be laid in successive layers, and each layer 
well settled with rammers. As this method is expensive, it 
is seldom resorted to except in works which require great 
care, and are of small extent. For extensive works, the 
method usually adopted is to embank out from one end, carry- 
ing forward the work on a level with the top surface. In 



"^'^IHWMIHIIHVWimr.JW'lHHnU 

"""""iiim)i[mii,nHiumiiiiim»!imnvw* w 
miruwriNmywuiHiwinniiiimimw^ 



Fig. 224. 



this case, as there must be a want of compactness in the 
mass, it is best to form the outsides of the embankment 
first, and to gradually fill in towards the middle, in order 
that the earth may arrange itself in layers with a dip 
towards the centre (Fig. 224). This arrangement will in a 



432 CIVIL ENGINEERING. 

great measure counteract the tendency of the earth sliding 
off in layers along the sides. 

586. Removal of the earth. — In both excavation and 
embankment, the problem is " to remove the earth from the 
excavation to the embankment or place of deposit by the 
shortest distance, in the shortest time, and at the least 
expense." This is an important problem in practice, and 
its proper solution affects Yery materially the cost of the 
work. 

The average distance to which the earth is carried to form 
the embankment is called the lead, and is assumed to be 
equal to the right line joining the centre of gravity of the 
volume of excavation with that of the embankment. When 
this lead is made the least possible, all other things being 
equal, the cost of removal of the earth is a minimum. 

In the execution of earthwork, it is not always advisable 
to make the whole of an embankment from the adjoining 
cuttings, as the lead would be too long. In such a case, a 
part of the cutting is wasted, being deposited in some conve- 
nient place, forming what is known as a spoil-bank. The 
necessary earth required to complete the embankment is 
obtained from some spot nearer to the work, and the cutting 
or excavation made in supplying it is called a borrow-pit. 

Means used to move the earth. — The earth is loosened 
by means of ploughs, picks, and shovels, and then thrown 
into wheelbarrows, carts, or wagons to be removed. A 
scraper drawn by a horse is frequently used to great advan- 
tage. 

Resort is sometimes had to blasting to loosen the soil, when 
it is rock, hard clay, and even frozen earth. 

The advantages of wheelbarrows over carts, and carts over 
wagons, etc., depend upon circumstances. When the dis- 
tance to transport the earth is considerable, the wheelbarrow 
becomes too expensive. By combining the cost of filling the 
cart or wheelbarrow, the amount removed, and the time 
occupied in transporting the earth, a comparison of the two 
methods can be made. 

Shrinkage. — When embankments are made in layers com- 
pacted by ramming or by being carted over, the subset pi ent 
settling is quite small. But made in the usual way, there is 
always a certain amount which must be provided for. This 
settling or shrinkage depends upon the kind of earth and the 
way the embankment has been made. 

This shrinkage of the different earths is taken to be about 
as follows, when compared with the space they occupied in 
the natural state : 



SIDE-HILL ROADS. 4:33 

Gravel shrinks about eight per cent. 

Gravel and sand nine per cent. 

Clay and clayey earth ten per cent. 

Loam and light earths twelve per cent. 

Rock, on the contrary, occupies more space, the percentage 
varying with the way it is heaped together. Carelessly 
piled its increase of volume was found to be seventy -five per 
cent., and carefully piled, fifty per cent. 

The embankment should always be made its full width and 
higher than it is intended to be. 

587. Methods of obtaining the quantities to be exca- 
vated, etc. — In comparing the costs of the routes or for 
rough estimates, it is sufficiently exact to take a number 
of equidistant profiles, and calculate the solid contents 
between each pair, either by multiplying the half sum of 
their areas by the distance between them, or else by taking 
the profile at the middle point between each pair, and 
multiplying its area by the same length as before ; the first 
of these methods gives too large a result, and the second too 
small. 

Where an exact estimate is to be made, the Prismoidal 
formula (Mensuration, p. 129) should be used. This formula 
gives the exact contents. 

588. In swamps and marshes. — When the embankment 
is made through a sw T amp or marsh, many precautions are 
necessary. 

If the bog is only three or four feet deep and has a hard 
bottom, it is recommended to remove the soft material and 
build the embankment on the hard stratum. 

If it be too deep to remove the soft material, its surface, 
provided it be not too soft, may be covered with some sub- 
stance to form an artificial bed for the embankment. Rows 
of turf with the grassy side downward have been used. 
Brushwood has also been tried. 

If the sw r amp be deep and the material quite fluid, the first 
thing to do is to drain it, and then prepare an artificial bed 
for the embankment. 

589. Side-hill roads. — When a road runs along the side 
of a hill, it is usually made half in excavation and half in 
embankment. But as the embankment is liable to slip if 
simply deposited on the natural surface of the ground, the 
latter should be cut into steps or offsets (Fig. 225). A low 
stone wall constructed at the foot of the embankment will add 
to its stability. 

If the surface of the hill be very much inclined, the side 
slopes of both the excavation and the embankment should be 
28 



434 



CIVIL ENGINEERING. 



replaced by retaining walls of dry stone (Fig. 226), or of stones 
laid in mortar. 

The upper wall may be dispensed with when the side hill 
is of rock. 




Fig. 225. 



When the road passes along the face of a nearly perpen- 
dicular precipice at a considerable height, as around a pro- 
jecting point of a rocky bank of a river in a mountainous 




Fig. 226. 



district, it may rest on a frame-work of horizontal beams let 
into holes drilled in the face of the precipice and supported 
at their outer ends by inclined struts beneath, the lower ends 
<>f which rest in notches formed in the rock. 



CROSS DRAINS. 435 



DRAINAGE. 



590. A system of thorough drainage, by which the water 
that filters through the ground will be cut off from the soil 
beneath the roadway, to a depth of at least three feet below 
the bottom of the road-covering, and by which the water 
falling upon the surface will be speedily conveyed off, before 
it can filter through the road-covering, is essential to the good 
condition of a road. 

The form of the road, the side drains, and the ditches (Fig. 
218), are arranged and constructed with this object in view. 
(Art. 556.) 

591. Covered drains or ditches. — As open ditches would 
be soon filled by the washings of the side-slopes in certain 
parts of the roads, covered drains (Fig. 227) are substituted 
for them in these places. 




Fig. 227. 

They may be constructed with a bottom of concrete, flag- 
ging, or brick, with sides of the same material, or as shown 
in the figure, and covered with flat stones, leaving open joints 
of about half an inch to give free admission to the water. The 
top'is covered with brushwood or with fragments of broken 
stone, or with pebbles and clean gravel, through which the 
water will filter freely without carrying any earth or sedi- 
ment into the drain. 

592. Cross drains. — Besides the covered drains parallel to 
the axis of the road in cuttings, other drains known as cross 
drains are made under the ror.dway. They should have a 
slope along the bottom to facilitate the escape of the water. 
A slope of 1 in 100 will be sufficient. 

They may be constructed in the same manner as the cov- 
ered drains, or trenches may be dug to the required depth 



436 CIVIL ENGINEERING. 

with the proper slope and filled with broken stone. On the 
stone a layer of brushwood is placed and over this the road- 
covering. Drains of this kind are known as blind ditches. 
Any construction will be effective which will leave a small 
open waterway at the bottom of the trench which will not be- 
come choked with sediment. 

If the road is level, the cross drains may run straight across, 
but if inclined they form a broken line, in plan the shape of 
the letter V, with the angular point in the centre of the road 
directed towards the ascent. From their form, they are 
termed eross-mitre drains. 

They are placed at intervals depending upon the nature 
of the soil and kind of road covering used, in some cases as 
much as sixty yards apart, in others not more than twenty 
feet. 

593. Catehwaters. — These are broad shallow ditches con- 
structed across the surface of the road so arranged that 
vehicles can pass over them easily and without shock. They 
are used to catch the water which runs down the length of 
the road and to turn it off into the side ditches. They are 
sometimes called water-tables. 

They are necessary on long slopes, and in depressions where 
a descent and an ascent meet, to prevent the water from cut- 
ting the surface of the road in furrows. In a depression, they 
are usually placed at right angles to the road ; on a slope, they 
cross the road diagonally where the water is to be carried to 
one side ; if to both sides, their plan is that of a V with the 
angular point up the road. 

The inclination of the bottom of the catch water should be 
sufficient to carry off the water as fast as it accumulates in 
the trench, and where the velocity of the current flowing 
through them is considerable, they should be paved. 

A mound of earth crossing the road obliquely is frequently 
used as a substitute for the catchwater. When used it should 
be arranged to allow carriages to pass over them without 
difficulty and inconvenience. 

594. Culverts. — These structures are used to carry under 
the road the water of small streams which intersect it, and 
also the water of the ditches on the upper side of a road to 
the lower side, or side on which the natural water-courses lie 
by which the water is finally carried away. 

They may be built of stone, brick, concrete, or even of 
wood. 

Where stone is scarce, a culvert may be built of planks or 
slabs, forming a long box open at the ends. This is a tem- 
porary structure unless it can be kept always wet. 



SIDEWALKS. 437 

A small full-centre arch of brick resting on a flooring of 
concrete forms a good culvert. 

The length of a culvert under an embankment will be 
equal to the width of the road increased by the horizontal 
distance on each side forming the base of the side-slope. At 
each end, wing-walls should be built, their faces having 
the same slope as that of the embankment. The ends of the 
culvert must be protected against the undermining action of 
the water. 

The form of cross-section varies according to the circum- 
stances of the case, depending greatly on the strength required 
in the structure and the volume and velocity of the water 
flowing through it. The dimensions of the waterway of a 
culvert should be proportioned to the greatest volume of 
water which it may ever be required to carry off, and should 
always be large enough to allow of a person entering it to 
clean it out. 

595. Footpaths and sidewalks. — Ordinarily, footpaths 
are not provided for in our country roads. They should be, 
however, and the remarks made in Art. 575 apply to their 
construction. 

In cities and towns, sidewalks and crossings are arranged 
in all the streets. They are made of flagging-stone, brick, 
wood, ordinary concrete, asphaltic concrete, etc. They 
differ in construction only in degree from roads of the same 
kind. 

596. Sidewalk of flagging-stone. — The flagstones are at 
least two inches in thickness, laid on a bed of gravel. The 
width of the sidewalk depends upon the numbers liable to 
use them, being wider where great crowds are frequent and 
less wide on streets not much used. A width of twelve feet 
is sufficient for most cases. 

The upper surface is not level, but has a slight slope to- 
wards the street to convey the surface water to the side 
channels. 

The pavement of the street is separated from that of the 
sidewalk by a row of long slabs set on their edges, termed 
curb-stones, which confine both the flagging and paving 
stones. The curb-stones form the sides of the side channels, 
and should for this purpose project six inches above the out- 
side paving stones, and be sunk at least four inches below 
their top surface ; they should be flush with the upper sur- 
face of the sidewalks, to allow the water to run over into the 
side channels, and to prevent accidents from persons tripping 
by striking their feet against them. 

The crossings should be from four to six feet wide, and be 



438 CIVIL ENGINEERING. 

slightly raised above the general surface of the pavement, to 
keep them free from mud. 



TRAM-ROADS. 

Tram-roads are built of stone, of wood, or of iron. 

597. Stone tram-roads. — The best tram-roads of stone 
consist of two parallel rows of granite blocks, about 4J feet 
apart from centre to centre, the upper surface of the blocks 
being flush with the surface of the road. The blocks should 
be from 4 to 6 feet long, 10 to 12 inches broad and 8 to 12 
inches deep. Sometimes the upper surface is made slightly 
concave for the purpose of retaining the wheels on the tracks. 

Stone tram-roads were used by the Egyptians, traces of 
them being found in the quarries which supplied stone for the 
pyramids. 

Tram-roads of stone have been used in England, and are 
used at the present time in Italy. 

The granite blocks used in the Italian tram-roads are from 
4 to 6 feet long, about 2 feet broad, and 8 inches deep, laid on 
a bed of gravel 6 inches thick. The space between the 
" trams " is paved with cobble stones with an inclination from 
the outside to the middle line. The centre is therefore lower 
than the sides, forming a channel for the water, which flows 
into cross drains provided to carry it off. 

In a tram-road on the Holyhead road, the granite blocks 
were required to be not less than 4 feet long, 14 inches broad, 
and 12 inches deep. The blocks were laid on a bed composed 
of a rough sub-pavement, similar to that used for the Telford 
road, on which was a layer three inches thick of small broken 
stone, and on top of this a layer of gravel two inches thick, 
compacted by a heavy roller. 

The effect of this tram-road was to reduce the amount of 
tractive force required more than one half of what was 
required on the broken stone road. 

598. Tram-roads of wood. — Where timber is plenty, tram- 
roads of wood are frequently used. They do not differ in 
principle of construction from the stone tramway. Since the 
wood is extremely perishable when buried in the damp 
ground, tramways of wood are used only in temporary con- 
structions. 

599. Iron tram-roads. — The iron tram-roads formerly used 
were made by covering a wooden track with flat iron bars, to 
increase the durability of the track and to lessen the resistance 
offered to the wheels. To keep the wheels on the track, a 



RAILROADS. 



439 



flange was placed on the side of the bar (Fig. 228). The 
objections to these tramways were the broad surface of the 
iron plate which collected obstructions upon it, and the fric- 
tion of the wheels against the flange. 





Fig. 228. 



Fig. 229. 



An iron plate (Fig. 229) is used quite extensively in the 
United States, particularly in Philadelphia, for tracks for 
street cars. The upper and narrower portion, a, is used by 
the wheels of the car, while the wider and flat portion, b, can 
be used by ordinary carriages. 



A4 



CHAPTEK XXIII. 



RAILROADS. 



600. As long as the flange attached to the bar was used to 
keep the wheels on the track, the road was called a tram-road. 
When the flange was removed from the bar and transferred 
to the wheel, the road became changed in character and was 
named a railway or railroad. The marked difference be- 
tween a tram-road and a railroad is, that the former is used by 
all classes of carriages, while the latter can be used only by 
cars specially built for the purpose. 

A railroad may be defined to be a track formed of iron or 
steel bars, called rails, placed in parallel lines, upon which 
rails the wheels of vehicles run. 

The general principles already alluded to as governing the 
location and construction of roads, apply equally to railroads, 
but in a higher degree. Greater importance is attached, for 
railroads, to straightness, to easy grades, and to using curves 
of larger radius where a change of direction takes place, than 
for any other kind of road. 

601. Direction. — Straightness of direction is more import- 



440 CIVIL ENGINEERING. 

ant for railroads than for common roads, for the reasons that 
the shorter the line the cheaper is its cost, and that there is 
a greater resistance offered by curves, causing a greater ex- 
penditure of tractive force. 

The same considerations which govern in determining the 
direction of a common road apply to the railroad, viz., cost of 
construction, wants of the community, etc. 

602. Grades. — The question of grade is more affected by 
the quality of economy than by practicability. Locomotives 
can be made to ascend steep grades by increasing their power 
and adhesion, but as the grades increase in steepness, the 
effective tractive force of the engine decreases. Thus with 
an ascent of 20 feet to the mile, an engine can draw about 
one-half the load which it can draw on a level ; at 40 feet to 
the mile, about one-third, etc. In these expressions, the mile 
is taken as the length of the slope, not the base. 

The cost of drawing a load on a railroad varies very nearly 
with the power employed. Hence it will cost nearly twice as 
much to haul a load on a grade of 20 feet to the mile as it 
would on a level road. This consideration will therefore 
justify large expenditures in the construction of the road with 
the view of reducing the grades. 

The steepest grade upon a given line is not necessarily the 
maximum inclination adopted for the road. It may be much 
greater and require special arrangements to be made to over- 
come it. 

The ruling or maximum grade adopted for the line depends 
upon the motive power used to ascend them and upon the 
avoidance of a waste of power in descending. 

When the loads to be carried in one direction over the road 
are much heavier than those carried in the other, the ascent 
up which the heavy loads are to be carried should be made by 
easy grades, while the descent may be made by steeper ones. 
If the travel is equal in both directions, the ruling grades 
should be equal for both slopes. 

The length of grades must be considered, as it is found 
more advantageous to have steep grades upon short portions 
of the line than to overcome the same difference of level by 
grades not so steep on longer developments. 

From various experiments, it appears that the , angle of 
repose (Art. 550) for a railroad is about yj-g-. But in de- 
scending grades much steeper than this, the velocity due to 
the accelerating force of gravity soon attains its greatest 
limit and remains constant, from the resistance caused by the 
air. 

The limit of the velocity thus attained, whether the train 



CURVES. 441 

descends by the action of gravity alone, or by the combined 
action of the motive power of the engine and gravity, can be 
determined for any given load. It appears from calculation 
and experiment that heavy trains, allowed to run freely 
without applying the brakes, may descend grades of t ^-q with- 
out attaining a greater velocity than about 40 miles an hour. 

Hence, the question to be considered in comparing the 
advantages of different grades is one of the comparative cost 
between the loss of power and speed for ascending trains on 
steep grades, and that of heavy excavations, tunnels, and 
embankments required by lighter grades. 

Since locomotives are not taxed to their full extent, grades 
of 60 feet to the mile may be used without any practical loss 
of power either in the ascent or 'descent. 

603. Curves. — Curves are necessary to enable the road to 
pass around obstacles, such as projecting hills, deep ravines, 
valuable houses which cannot be removed, etc. 

The objections to curves in the road are the resistances 
which they offer to the motion of the cars and the dangers to 
which they expose them. 

The resistances offered by the curves are chiefly due to the 
following causes : , 

1. The obliquity of the moving power while passing around 
the curve. 

2. The friction of the flanges of the wheels against the 
outer rail due to the centrifugal force. 

3. The friction of the flanges against the rails due to the 
parallelism of the axles. 

4. The fastening of each pair of wheels to the same axle. 
The danger of a car running off the track is much increased' 

by curves. The car is kept on the rails while going around 
a curve by the flanges of the wheels and the firmness of the 
outer rails. If the resistance offered by the rails and flanges 
should be overcome by the " quantity of motion " of the car, 
it would leave the track. Hence, where sharp curves are 
necessary, they should be located, if possible, near stopping 
places, and never at those points where the speed is to be very 
high or where the car will come with great velocity, like that 
at the foot of a steep grade. 

The minimum radius of a curve depends greatly upon the 
speed to be employed. In France, the minimum radius 
allowed is 2,700 feet. In England, no curve less than 2,640 
feet can be used without special permission of Parliament or 
the Board of Trade. The minimum radius used on the Hud- 
son River Railroad is 2,062 feet. On the Baltimore and Ohio 
Railroad, the minimum radius is 600 feet, although when first 



442 CIVIL ENGINEERING. 

constructed there were several curves of 400 feet radius, and 
one of 318 feet over which trains passed at a speed of 15 
miles an hour. 

604. Resistances of vehicles on railroads. — The resist- 
ance offered to the force of traction by a train of cars is due 
to friction, concussion, and the atmosphere. The amount 
of this resistance depends upon a variety of conditions, such as 
the condition of the road, whether well or badly constructed, 
in bad order, etc. ; the state of the rolling machinery ; the 
climate ; the season of the year ; state of the weather, etc. 

In discussing the resistance, it is assumed that the cars are 
well made, the track in good order, and the weather moder- 
ately calm. The amount of resistance may be determined by 
means of a dynamometer between the engine and the train, 
and may be expressed either as a fraction or as a certain num- 
ber of pounds per ton, the latter being generally used. 

That part of the resistance offered by the train due to 
friction is constant at all speeds ; that due to concussion and 
the atmosphere varies with the velocity, increasing with the 
speed. The law of increase is not fully known. 

605. On a level and straight road. — The resistance 
offered by a train running on a level and straight road, nearly 
as possible under the conditions in ordinary practice, has been 
determined by experiment to be nearly that given by the 
following formula : 

r = ~ + 8, . . . . (173) 

in which r is the resistance in pounds per ton of the engine? 
tender, and train ; and v the velocity in miles per hour. 

Hence it is seen, that for a train moving at the rate of 20 
miles an hour, the resistance would be 10.33 pounds per ton 
of the entire train. 

If the road is in bad repair, the values obtained by this 
formula should be increased 40 per cent. ; for strong side 
winds, 20 per cent. 

606. Resistance due to grades. — The resistance due to 
a grade is found by multiplying the whole weight of the train 
by the difference of level and dividing this product by the 
length of the slope. By this rule it is found that the resist- 
ance per ton due to a grade of 24 feet in a mile is 

24 
2,240 x -^ = 10.2 pounds, 

or about the same as that on a level with the speed of 20 
miles an hour. Therefore, if the train runs over this grade at * 



443 

20 miles an hour, the resistance would be jnst double, or it 
would require the same power to run one mile on the grade 
that would draw the same load at the same speed two miles 
on a level road. 

607. Resistance due to curves. — The resistance due to 
curvature is much affected by the gauge of the road, the ele- 
vation of the outer rail, the form of surface of the tires and 
the size of the wheels, the speed and length of the train, etc. 
Hence, experiments made to obtain this resistance will be 
found to vary greatly for the same curve on different roads. 
The point to be gained, however, is to find the amount of 
curvature which will consume an amount of power sufficient 
to draw a train one mile on a straight and level road. 

It is assumed that the resistance from curvature is inversely 
as the radius ; that is, the resistance offered by a curve of 2° 
is double that of a curve of 1°. 

From experiments made under his direction, Mr. Latrobe 
deduced the resistance upon a curve of 400 feet radius to be 
double that upon a straight line. 

Upon averaging a large number of experiments made for 
this purpose, it is found that a radius of 574 feet, or curve of 
10°, offers a resistance to a train travelling at the rate of 20 
miles an hour, double that on a straight and level line, at the 
same speed. Hence a curve of ten degrees causes a resist- 
ance of ten pounds to the ton. Knowing this resistance, that 
for any other curve is easily obtained. 

If we desire to make the resistance uniform upon any sys- 
tem of grades and curves, it will be necessary, whenever a 
curve occurs upon a grade, to reduce the latter to an amount 
sufficient to compensate for the resistance caused by the 
curve. 

608. Mr. Scott Russell's formula. — Formula (173) gives 
the value of the total resistance without separating it into its 
parts. 

The formula of Mr. Russell and Mr. Harding gives separate 
expressions for each resistance. This formula is as follows : 

7 ,2A 

r = 6W + fc>W + m ,. ■ . (174) 

in which r and v are the same as in (173), W, the weight of 
the train in tons, and A, the area of frontage of the train in 
square feet. 

This formula may be expressed in words, as follows : 

1. Multiply the weight in tons by 6. The product will be 
the amount in pounds due to friction. 

2. Multiply the weight in tons by the velocity in miles per 



444 CIVIL ENGINEEKING. 

hour and divide the product by 3. The result will be the 
amount in pounds due to concussion. 

3. Multiply the square of the velocity in miles per hour by 
the frontage of the train in square feet and divide the pro- 
duct by 400. The result will give the resistance in pounds 
due to the atmosphere. 

4. Add these three results, and the sum is the total resist- 
ance. Divide the total resistance by the weight, and the quo- 
tient is the resistance per ton. 

The foregoing results corresponded closely with the experi- 
ments for speed from 30 to 60 miles per hour. At lower rates 
of speed, the rule gave too great results. 

Another formula in which the resistance of the atmosphere 
is assumed to be proportional to the volume of the train has 
been used. It is as follows : 



r=(6 +I6 )w +wm , . . (175) 



in which B is the volume of the train, the other quantities 
being the same as in (174). 

609. Tractive force. — The forces employed to draw the 
cars on railroads are gravity, horses, stationary engines, and 
locomotive engines. 

610. Gravity. — Gravity either assists or opposes the other 
kinds of motive power on all inclined parts of a railroad. It 
may be used as the sole motive power on grades which are 
sufficiently steep. In this case the loaded cars descending the 
grade draws up a train of empty ones. The connection is 
made between the trains by means of a wire rope which runs 
over pulleys placed along the middle of the track. 

611. Horses. — Horses are frequently used to draw cars on 
a railroad. 

The power of a horse to move a heavy load is ordinarily 
assumed at 150 pounds, moving at the rate of 2J miles an 
hour for 8 hours a day. At greater speeds his power of 
draught diminishes, drawing only half his load at 4 miles an 
hour, etc. 

The power of the horse is rapidly diminished upon ascents. 
On a slope of 1 in 7 (8£°) he can carry up only his own 
weight (Gillespie). 

612. Stationary engines. — These are employed sometimes 
where the speed is to be moderate, the grade is steep, and the 
distance short. 

The power is usually applied to an endless wire rope run- 
ning on pulleys, like that employed where gravity is the 

force used. And as in that case, the descent of one train is 

> . 



LOCOMOTIVE ENGINES. 445 

used to assist in drawing the other to the top of the inclined 
plane. 

613. Locomotive engines. — The principal motive power 
on railroads is the locomotive engine. 

The locomotive is a non-condensing, high-pressure engine, 
working at a greater or less degree of expansion according to 
circumstances, and placed on wheels which are connected 
with the piston in such a manner that any motion of the latter 
is communicated to them. 

The power exerted in the cylinder and transferred to the 
circumference of the driving wheel is termed " traction ; " 
its amount depends upon the diameter of the cylinder, the 
pressure of the steam, the diameter of the driving wheel, and 
the distance, called the stroke, traversed by the piston from 
one end of the cylinder to the other. 

The means by which the traction is rendered available for 
moving the engine and its load is the resistance which the 
driving wheels offer to slipping on the rail ; this is called the 
" adhesion," and its amount varies directly with the load rest- 
ing on the wheels, and depends upon the condition of the 
surface of the rails, being almost nothing when ice is on the 
rails, and as much as one-fifth of the weight on the driving 
wheels when the surface of the rail is clean and dry. 

The speed of the engine depends also upon the rapidity 
with which its boiler can generate steam. One cylinder full 
of steam is required for each stroke of the piston. Each 
double stroke corresponds to one revolution of the driving 
wheels and to the propulsion of the engine through a space 
equal to their circumference. 

Steam-producing-, adhesion, and traction, are the three 
elements which determine the ability of a locomotive engine 
to do its work. The work required of the engine depends 
upon the nature and amount of the traffic over the road and 
the condition of the road. Hence, engines of different pro- 
portions are employed on the same road, one set to haul heavy 
loads at low velocities and another set to move light loads at 
high rates of speed. 

Stronger and more powerful engines are needed on a road 
with steep grades and sharp curves than on roads with easy 
grades and large curves. 

Locomotive engines may be so proportioned as to run at any 
speed from to 60 miles an hour ; to ascend grades up to as 
high as 200 feet in the mile ; and to draw from 1 to 1,000 
tons. 

The weight and speed of the trains, and the ruling grades 
of the road determine the amount of power required of the 



446 CIVIL ENGINEERING. 

engine. , This power depends, as has just been stated, upon 
the steam-producing capacity of the boiler, upon the leverage 
by which the steam is applied, and upon the adhesion. 

614. Gauge. — The width of a railroad between the inner 
sides of the rails is called the gauge. 

The question as to what this width should be has been a 
subject for discussion and of controversy among engineers. 

The original railroads were made of the same width as the 
tram-roads on which the ordinary road wagon was used. It 
happened that the width of the tram-road was 4 feet 8 J- inches, 
which was adopted for the railroad, and soon became univer- 
sal. In a few cases, other widths were adopted, but the ad- 
vantages of uniformity so far exceed all other considerations, 
that the widtli of 4 feet 8J inches is now generally adopted 
for roads of the first class or main lines. 

For branch lines, a still narrower gauge is recommended ; 
a width of 3 feet, and even of 2 feet 6 inches, has been em- 
ployed. A road of this narrow gauge costs less to construct 
and admits of steeper grades and sharper curves being used. 

Railroads may have either a single or a double track. 
When first constructed and where the traffic is light, a single 
track is used, but even then it is recommended to take suffi- 
cient ground to provide for the second track when it becomes 
necessary. 

The New York Central Railroad has four tracks, two of 
which are used for passenger traffic and two for movement 
of freight. 

LOCATION AND CONSTRUCTION OF RAILROADS. 

615. Location. — Location of railroads is guided by the same 
principles as that of ordinary roads and is made in the same 
manner. The greater importance to railroads of easy grades 
and straightness justifies a greater expenditure for surveys, 
which are more elaborate than those required for common 
roads. 

016. Construction. — This may be divided into two parts : 
" forming the road-bed," and the " superstructure." 

The remarks already made concerning the " construction of 
roads" apply to "forming the road-bed of a railroad." 

The excavations and embankments are generally much 
greater on railroads than for any other of the roads usually 
constructed. Where, for instance, an ordinary road would 
wind around a hill, a railroad would cut through it, in this 
way obtaining straightness and avoiding curves. 
* The sides of an excavation is often supported by retain- 



SHAFTS AND TUNNELS. 447 

ing walls in order to reduce the width of the cutting at the 
top. 

617. Tunnels. — The depth of excavation is oftentimes so 
great that it will frequently be found cheaper to make a pas- 
sage under ground called a tunnel. 

The choice between deep cutting and tunnelling will de- 
pend upon the relative cost of the two and the nature of the 
ground. When the cost of the two methods would be about 
equal, and the slopes of the deep cut are not liable to slips, it is 
usually more advantageous to resort to deep cutting than to 
tunnelling. So much, however, will depend upon local circum- 
stances, that the comparative advantages of the two methods 
can only be decided by a careful* consideration of these cir- 
cumstances for each particular case. Where a choice may be 
made, the nature of the ground, the length of the tunnel, that 
of the deep cuts by which it must be approached, and also the 
depths of the working shafts, must all be well studied before 
any decision can be made. In some cases it may be found 
that a longer tunnel with shorter deep cuts will be more ad- 
vantageous in one position than a shorter tunnel with longer 
deep cuts in another. In others, the greater depth of working 
shafts may be more than compensated by obtaining a safer 
soil, or a shorter tunnel. 

As a general rule tunnelling is to be avoided if possible. 

The dimensions and form of the cross-section will depend 
upon the nature of the soil and the object of the tunnel as a 
communication. In solid rock, the sides of the tunnel are 
usually vertical, the top curved, and the bottom horizontal. 
In soils which require to be sustained by an arch, the exca- 
vation should conform as nearly as practicable to the form 
of cross-section of the arch. 

* In tunnels through unstratified rocks, the sides and roof 
may be left unsupported ; but in stratified rocks there is 
danger of blocks becoming detached and falling : wherever 
this is to be apprehended, the top of the tunnel should be 
supported by an arch. 

In choosing the site of a tunnel, attention should be had, 
not only to the nature of the soil, and to the shortness and 
straightness of the tunnel, but also to the facilities offered for 
getting access to its course at intermediate points by means of 
shafts and drifts. 

618. Shafts. — Vertical pits which are sunk to a level with 
the crown or top of the tunnel are known as shafts. 

There are three kinds : trial, working, and permanent 
shafts. 

Trial shafts are, in general, sunk at or near the centre line 



448 CIVIL ENGINEERING. 

of the proposed tunnel to ascertain the nature of the strata 
through which the tunnel is to be excavated. Their dimen- 
sions and shape are regulated by the uses to which they are to 
be put. 

Working shafts are used to give access to the tunnel, for 
the purpose of carrying on the work and removing the mate- 
rial excavated, for admitting fresh and discharging foul air, 
and for pumping out water. 

Their dimensions will be fixed by the service required of 
them. Their distance apart varies between 50 and 300 yards, 
although in some cases they were only from 20 to 30 yards 
apart, and in others none were used. 

They may b'e located along the centre line of the tunnel or 
they may be on a line parallel to it. 

Permanent shafts are generally working shafts that have 
been made permanent parts of the tunnel for the purposes of 
ventilation and of admitting light. 

619. Drifts. — Small horizontal or slightly inclined under- 
ground passages made for the purpose of examining the strata, 
for the purpose of drainage, of affording access to the tunnel 
for the workmen and for transport of materials, etc., are 
termed drifts or headings. 

Their least dimensions are those in which miners can con- 
veniently work, or from 4J to 5 feet high and 3 feet wide. 

Headings are almost always nsed to connect the working 
shafts, running along the centre line or parallel to the line 
of the tunnel. In soft ground, the heading is at or near the 
bottom -of the tunnel; in rock or hard and dry material at or 
near the top. 

620. Laying out tunnels. — The establishment of a correct 
centre line for a tunnel and fixing the line at the bottom of 
the shafts are most important operations and require the 
utmost care. 

The work is commenced by setting out, in the first place, 
w T ith great accuracy upon the surface of the ground, the pro- 
file line contained in the vertical plane of the axis of the 
tunnel, and at suitable intervals along this line, sinking work- 
ing shafts. At the bottom of these shafts the centre line is 
marked out by two points placed as far apart as possible. By 
these the line is prolonged from the bottom of the shaft in 
both directions. 

In constructing the Iloosac Tunnel, so accurate were the 
alignments, that the heading running eastward from the 
central shaft for a distance of 1,5.63 toot met the heading 
from the eastern end with an error of hut five-sixteenths of 
an inch; and the heading running west ward for 2,056 feet 



DRAINAGE AND VENTILATION. 449 

met the heading from the western end with an error of bnt 
nine-sixteenths of an inch. 

An elaborate trignometrical survey was used to lay out the 
Mont Cenis Tunnel, which was 7.5 miles long, with no work- 
ing shafts. 

621. Operation of tunnelling. — The shafts and the ex- 
cavations which form the entrances to the tunnel 'ire con- 
nected by a drift, usually five or six feet in width and seven 
or eight feet in height, made along the crown of the tunnel 
when the soil is good. After the drift is completed, the 
excavation for the tunnel is gradually enlarged ; the ex- 
cavated earth is raised through the working shafts, and 
at the same time carried out at the ends. The speed with 
which the drift is driven determines the rate of progress of 
the whole. 

If the soil is loose, the operation is one of the most hazard- 
ous in engineering construction, and requires the greatest pre- 
cautions against accident. The sides of the excavations must 
be sustained by strong rough frame-work, covered by a sheath- 
ing of boards to secure the workmen from danger. When in 
such cases the drift cannot be extended throughout the line 
of the tunnel, the excavation is advanced only a few feet in 
each direction from the bottom of the working shafts, and 
is gradually widened and deepened to the proper form and 
dimensions to receive the masonry of the tunnel, which is 
immediately commenced below each working shaft, and is 
carried forward in both directions towards the two ends of 
the tunnel. 

In some cases, two headings were run forward and the side 
walls of the tunnel were built before the remainder of the 
section was excavated. \ 

The ordinary difficulties of tunnelling are greatly increased 
by the presence of water in the soil through which the work 
is driven. Pumps, or other suitable machinery for raising 
water, placed in the working shafts, will, in some cases, be 
requisite to keep them and the drifts free from water until an 
outlet can be obtained for it at the ends, by a drain along the 
bottom of the drift. 

62X. Drainage and ventilation of tunnels. — The drain- 
age of a tunnel is effected either by a covered drain under the 
road-bed at the centre or by open drains at the sides. 

Artificial ventilation is found not to be necessary in ordinary 
tunnels, and the permanent shafts constructed for the purpose 
have been considered detrimental rather than beneficial in 
getting rid of the smoke. The passage of the train appears 
to be the best ventilator ; the air being thoroughly disturbed 
29 



450 



CIVIL ENGINEERING. 



and displaced by the quick motion of the train through the 
tunnel. 

623. Ballast. — The tops of the embankments and the bot- 
tom of the excavations are brought to a height called the 
" formation level," about two feet below the intended level of 
the rails. The remaining two feet, more or less, is filled up 
with gravel, or gravel and sand, or broken stone, or similar 
material, through which the water will pass freely. This 
layer is called the " ballast," and the material of which it is 
composed should be clean and hard, so as not to pack into a 
solid mass preventing the water from passing through it. 

The object of the ballast, besides allowing the water to run 
off freely, is to hold the sleepers firmly in their places and to 
give elasticity to the road-bed. 

624. Cross ties. — The cross ties or " sleepers " are of wood, 
hewn flat on the top and bottom ; they are from 7 to 9 'feet 
long for the ordinary gauge, 6 inches deep, and from 6 to 10 
inches wide. The distance between the ties depends upon 
the weight of the engines used on the road and the strength 
of the rail; 2-J feet from centre to centre is about the 
usual distance. The nearer the sleepers are to uniformity in 
size and to being equidistant from each other, the more uni- 
form w^ill the pressure from the passage of the train be 
distributed over the ground. 

The sleepers may be of oak, pine, locust, hemlock, chest- 
nut, etc. They last from 5 to 10 years, depending upon their 
positions and the amount of travel over them. Their duration 
may be increased by using some of the preservative means 
referred to in Art. 25. 

625. Rails. — The rails are made of wrought iron, of 
wrought iron with a thin bar of steel forming the top surface, 
or made entirely of steel. 

Since the rail acts as a support for the 
train between the ties, and as a lateral 
guide for the wheels, it must possess 
strength and stiffness to a marked degree. 
The top surface should be of sufficient 
size and hardness to withstand the action 
of the rolling loads, and the bottom surface 
should be wide enough to afford a good 
bearing upon the tie. The rail should 
have that form which gives the required 
strength with the least amount of mate- 
rial. The form of cross-section in most general u>e at the 
p refent time in the United States is shown in Fig. 2 10. This 
particular rail is 4J inches high and 4 inches wi le at the 




Fig. 230. 






ELEVATION OF THE OUTER RAIL. 451 

bottom. The width of the head varies from 2^ to 2-J inches 
the top surface having a convex form, circular in cross- section, 
described with a radius double the height of the rail. The 
thickness of the rib or stem is generally from i to } of an 
inch, although recent experiments would indicate that a less 
thickness might be used with safety. 

The rails are rolled in lengths varying from 15 to 21 feet, 
and when laid are connected by fish-joints and fastened to 
the cross-ties by spikes. The method of fastening formerly 
used was to confine the ends of the rails in a cast-iron chair 
which rested on the cross-ties. This method may be seen on 
some of the older railroads, but is fast going out of use on 
all first-class roads. 

When the track is straight, a line drawn in the cross- 
section made by a plane perpendicular to the axis of the 
road, tangent to the upper surfaces of the rails, is horizontal. 
When the track is curved, this line is inclined : that is, the 
tops of the rails are inclined, or given a "cant. ,; The amount 
of inclination depends upon the amount of conical form given J 
to the tread of the wheel. For the common gauge, iHs taken 
at about -^t- 

626. Coning of the wheels. — The wheel running on the 
outer rail of a curve has to pass over a greater distance than 
the one running on the inner rail. Since the wheels and axles 
are firmly connected, some arrangement must be made to keep 
the wheels from dragging or slipping on the rails and to re- 
duce the twisting strain brought on the axles. This is usually 
effected by making the tread of the wheel conical instead of 
cylindrical, so that the tendency of the car to press against 
the outer rail brings a larger diameter upon the outer and a 
smaller diameter on the inner rail. The difference between 
these diameters must be proportioned to the distance to be 
traversed by the wheels, and must depend therefore, upon 
the radius of the curve and the gauge. The sharper the curve, 
the greater should be the difference between the diameters. 
Upon many roads it is customary to widen the gauge from 4 
feet 8-J- inches to 4 feet 9 inches on sharp curves, thus allowing 
more play for the wheels and giving a greater difference in the 
diameters of those parts of the wheel in contact with the rails. 

627. Elevation of the outer rail. — On the curved por- 
tions of the track the centrifugal force tends to throw the car 
against the outer rail. This tendency is resisted by raising 
the outer rail to a certain height above the inner one. The rule 
for obtaining this height is expressed as follows : 

h =£k> m 



452 



CIVIL ENGINEERING. 



in which h is the elevation above inner rail in inches ; v, the 
velocity in feet per second ; g, the gauge of the road in 
inches ; and R, the radius of the curve in feet. 

628. Crossings, switches, etc. — To enable trains to pass 
from one track to the other, crossing's are arranged as shown 
in Fig. 231. The connection between the crossing and the 
track is made by a switch. 




Fra. 231. 

The switch consists of one length of rails, movable around 
one of the ends, so that the other can be displaced from the 
line of the main track and joined with that of the crossing, or 
the reverse, depending upon which line of rails the train is to 
run. A vertical lever is attached to the movable end by 
means of which the ends of the rails are pushed forward or 
shoved back, making the connection with the tracks. The 
handles of the lever should be so fashioned and painted that 
their position may be seen from, a considerable distance. 

Where one line of rails crosses another, an arrangement 
called a crossing-plate, or frog (Fig. 232), is used to allow 
free passage of the wheels. 




Fig. 232. 



In order that the wheels should run smoothly on the rail 
A B, the rail C D must be cut at its intersection with the 
former; for a similar reason, the rail A B must be cut at its 
intersection witli C D. 

A guard-rail, G G, is used to confine the opposite wheel for 
short distance and prevent the wheel running on A B from 
leaving the rail at the cut. This guard-rail is parallel to the 



NAVIGABLE CANALS. 453 

outer rail and placed about two inches from it. It extends 
a short distance beyond the opening in both directions and 
has its ends curved slightly, as shown in Fig. 231. 

The angle between the lines of the main track and the 
crossing should be very small, not greater than 3°. 

629. Turn-tables. — When the angle is too great to use the 
crossing, the arrangement called a turn-table is employed. 
This consists of a strong circular platform of wood or iron, 
movable around its centre by means of conical rollers beneath 
it running upon iron roller- ways. Two rails are laid upon 
the platform to receive the car, which is transferred from one 
track to the other by turning the platform sufficiently to place 
the rails upon it in the same line with those of the track upon 
which the car is to run. The greater the proportion of the 
weight borne by the pivot at the centre and the less that 
borne by the rollers, the less will be the friction. 

630. Telegraph, mile-posts, etc. — On all well managed 
railroads, telegraph lines are essential to the safe working of 
the road. These should be connected with every station. By 
their use, the positions of the different trains at all hours are 
made known. 

Mile-posts, numbered in both directions, should be placed 
along the sides of the road. Posts showing the grades, the 
distance to crossings of roads, to bridges, etc., should be used 
wherever necessary. 



CHAPTEK XXIV. 

CANALS. 

631. A canal is an artificial water-course. Canals are 
used principally for purposes of inland navigation ; for irriga- 
tion ; for drainage ; for supplying cities and towns with 
water, etc. 

NAVIGABLE CANALS. 

632. Navigable canals may be divided into three classes ; 
level canals, or those which are on the same level through- 
out ; lateral canals, or those which connect two points of 
different levels, but have no summit level ; and canals with 
a summit level, or those connecting two points which lie 
on opposite sides of a dividing ridge. 



4:54 CIVIL ENGINEERING. 

I. Level canals. — In canals of this class, the level of the 
water is the same throughout. As in roads, straightness of 
direction gives way to economy of construction, and the econ- 
omical course will be that which follows a contour line, 
unless a great saving may be made by using excavation or 
embankment. Where changes of direction are made, the 
straight portions are connected by curved ones, generally arcs 
of circles, of sufficient curvature to allow the boats using the 
canal to pass each other without sensible diminution in their 
rate of speed. 

II. Lateral canals. — In these canals, the fall of water is in 
one direction only. Where the difference of level between the 
extreme points is considerable, the canal is divided into a 
series of levels or ponds, connected by sudden changes of 
level. These sudden changes in level are overcome by means 
of locks or other contrivances by which the boat is transferred 
from one level to the other. 

III. Canals "with summit levels. — These are canals in 
which the points connected are lower than the intermediate 
ground over which the canal has to pass, and in consequence 
the fall is in both directions. As the water for the supply of 
the summit level must be collected from the ground which 
lies above it, it follows that the summit level should be at the 
lowest point of the ridge dividing the two extremes of the 
canal. 

633. Form and dimensions of water-way. — The general 
width of a canal should be sufficient to allow two boats to 
pass each other easily. Where great expense would be in- 
curred in giving this width, like that of a bridge supporting a 
canal, short portions may be made just wide enough for one 
boat. 

The depth should be such as not to materially increase the 
resistance to the motion of the boat beyond what is felt in 
open water. 

The bottom of the canal is generally made horizontal. The 
sides are inclined, and when of earth should not be steeper 
than one upon one and a half; if of masonry, the sides may 
be vertical or nearly so. In the latter case a greater width 
must be given to the bottom of the canal. 

The water-way is usually of a trapezoidal form, in cross- 
section (Fig. 233) with an embankment on each side, raised 
above the general surface of the country and formed of the 
material from the excavation for the canal. 

The relative dimensions of the parts of the cross-section 
may be generally stated as follows: 



TOWPATII. 



455 



The width of the water-way, at bottom, should be at least 
twice the width of the boats used in navigating the canal. 

The depth of the water-way should be at least eighteen 
inches greater than the greatest draft of the boat. 




: — ^ 

Fig. 233. — A, water-way. B, towpath. C, berm. D, side-drain. E, 
puddling of clay. 

The least area of water-way should be at least six times the 
greatest midship section of the boat. 

634. A towpath for horses is made on one of the em- 
bankments and a footpath on the other. This footpath should 
be wide enough to serve as an occasional towpath. 

The towpath should be from ten to twelve feet wide, to 
allow the horses to pass each other with ease ; and the foot- 
path at least six feet wide. The height of the surfaces of 
these paths, above the water surface, should not be less than 
two feet, to avoid the wash of the ripple ; nor greater than 
four feet and a half, for the facility of the draft of the 
horses in towing. The surface of the towpath should incline 
slightly outward, both to convey off the surface water in wet 
weather and to give a firmer footing to the horses, which 
naturally draw from the canal. 

The width given to these paths will give a sufficient thick- 
ness to the embankments to resist the pressure of the water 
against them, and to prevent filtration through them, provided 
the earth is at all binding in its composition. 

635. Construction. — All canal embankments should be 
carefully constructed. The earth of which they are formed 
should be of a good binding character, and perfectly free 
from mould and all vegetable matter, as the roots of 
plants, etc. In forming the embankments, the mould should 
first be removed from the surface on which they are to 
rest, and the earth then spread in uniform layers, from 
nine to twelve inches thick, and well rammed. If the char- 
acter of the earth, of which the embankments are formed, is 
such as not to present entire security against filtration, a pud- 
dling of clay, two or three feet thick, should be laid in the 
interior of the mass, extending from about a foot below the 
natural surface up to the same level with the surface of the 
water. Sand is useful in stopping leakage through the holes 



456 



CIVIL ENGINEERING. 



made in the embankments near the water surface by insects, 
moles, rats, etc. 

The side slopes of the embankment vary with the character 
of the soil : towards the water-way they should seldom be less 
than two base to one perpendicular; from it, they may be 
less. The interior slope is usually not carried up unbroken 
from the bottom to the top ; but a horizontal space, termed a 
"bench or berm, about one or two feet wide, is left, about one 
foot above the water surface, between the side slope of the 
water-way and the foot of the embankment above the berm. 
This space serves to protect the upper part of the interior 
side slope, and is, in some cases, planted with such shrubbery 
as grows most luxuriantly in moist localities, to protect more 
efficaciously the banks by the support which its roots give to 
the soil. The side slopes are better protected by a revetment 
of dry stone, from six to nine inches thick. Aquatic plants 
of the bulrush kind have been used, with success, for the 
same purpose ; being planted on the bottom, at the foot of 
the side slope, they serve to break the ripple, and preserve 
the slopes from its effects. 

Side drains must be made, on each side, a foot or two from 
the embankments, to prevent the surface water of the natural 
surface from injuring the embankments. 

636. Slight leakage may sometimes be stopped by sprinkling 
fine sand in small quantities at a time over the surface of the 




Fig. 234. 



water in the vicinity of the leaks. The sand settling to the 
bottom gradually fills the crevices in the sides and bottom of 
the canal through which the water escapes. 

The leakage may be so great that it may be necessary, in 
certain cases, to line the canal with masonry, concrete, or to 
face the sides with sheet- piling to retain the water. 

When the bottom of the canal is composed of fragments 
of rock forming large crevices, or composed of mail, it lias 
been frequently found necessary to line t lie water-way in such 
localities with masonry (Fig. 234) or with concrete. 



LOCKS. 



457 



In a lining of this kind, the stone used was about four 
inches thick, laid in cement or hydraulic mortar, and covered 
with a coating of mortar two inches thick, making the entire 
thickness of the lining six inches. This lining was then covered, 
both at bottom and on the sides, by a layer of earth, at least 
three feet thick, to protect it from the shock of the boats strik- 



ing against it. 



637. Size of canals. — The size of a canal depends upon the 
size of the boats to be used upon it. The dimensions of com- 
mon canal boats have been fixed with a view of horses being 
used to draw them. The most economical use of horse-power 
is to draw a heavy load at a low rate of speed. Assuming a 
speed of from two to two and a half miles an hour, a horse 
can draw a boat with its load, in all about 170 tons. This 
requires a boat of the ordinary cross-section to be about twelve 
feet wide, and a draught of four and a half feet when fully 
loaded. 

Boats of greater cross-section are frequently used, and are 
drawn by various applications of steam as well as by horse- 
power. The methods used are various, as the screw propeller, 
stationary engines with endless wire ropes, etc. Canals are 
sometimes made only twelve feet wide at bottom, with a 
draught of four feet ; common canals are from twenty-five to 
thirty feet wide at bottom, and a depth of from five to eight 
feet ; ship or large canals are fifty feet wide at bottom, and: 
have a depth of twenty feet. These are the minimum dimen- 
sions. 

638. Locks. — An arrangement termed a lock is ordinarily, 
used to pass a boat from one level to another. 

A lock is a small basin just large enough to receive a boat,, 
in which the water is usually confined on the sides by two 




upright walls of masonry, and at the ends by two gates, 
which open and shut, both for the purpose of allowing the 
boat to pass and to cut oft' the water of the upper level from 
the lower, as well as from the lock while the boat; is in it; 

A lock (Figs. 235 and 236) may be divided into* three dis- 
tinct parts : 1st. The part included between the two gates, . 



4:58 CIVIL ENGINEERING. 

which is termed the chamber. 2d. The part above the 
* upper gates, termed the fore or head-bay. 3d. The part 
below the lower gates, termed the aft or tail-bay. 

Fig. 235 shows a vertical longitudinal section through the 
axis of a single lock built on a foundation of concrete,* and 
Fig. 236 represents the plan. 



k 



Fig. 236. 



In these figures, A is the lock-chamber ; E, E, the side 
walls ; B, the head-bay ; C, the tail-bay ; and D, the lif t-wall. 

The lock-chamber must be wide enough to allow an easy 
ingress and egress to the boats commonly used on the canal ; 
a breadth of one foot greater than the greatest breadth of 
the boat is deemed sufficient for this purpose. The length 
of the chamber is regulated by that of the boats ; it should 
be such that when the boat enters the lock from the lower 
level, the tail-gates may be shut without requiring the boat 
to unship its rudder. 

The plan of the chamber is usually rectangular, the sides 
receiving a slight batter ; as when so arranged they are found 
to give greater facility to the passage of the boat than when 
vertical. The bottom of the chamber is either flat or curved ; 
more water will be required to fill the flat-bottomed chamber 
than the curved, but it will require less masonry in its con- 
struction. 

The chamber is terminated just within the head-gates by 
a vertical wall, the plan of which is usually curved. As this 
wall separates the upper from the lower level, it is termed 
the life- wall ; if is usually of the same height as the lift of 
the levels. The top of the lift-wall is formed of cut stone, 
.the vertical joints of which are normal to the curved face of 
the wall ; this top course projects from six to nine inches 
above the bottom of the upper level, presenting an angular 
point for the bottom of the head-gates, when shut, to rest 
against. This projection is termed the mitre-sill. Various 
degrees of opening have been given to the angle between the 
two branches of the mitre-sill; it is, however, generally ^o 



locks. 459 

determined, that the perpendicular of the isosceles triangle, 
formed by the two branches, shall vary between one-fifth and 
one-sixth of the base. 

The side-walls sustain the pressure of the embankment 
against them, and when the lock is full the pressure from the 
water in the chamber. The former pressure is the greater 
and the more permanent of the two and the dimensions of the 
wall are determined to resist this pressure. The usual man- 
ner of doing this is to make the wall four feet thick at the 
water line of the upper level, to secure it against filtration ; 
and then to determine the base of the batter, so that the mass 
of masonry shall present sufficient stability to resist the thrust 
of the embankment. The spread and other dimensions of 
the foundations w r ill be regulated according to the nature of 
the soil, as in other masonry structures. 

The bottom of the chamber, as has been stated, may be 
either flat or curved. The flat bottom is suitable to firm 
soils, which will neither yield to the vertical pressure of the 
chamber walls nor admit the water to filter from the upper 
level under the bottom of the lock. In either of these cases, 
where yielding or undermining may be expected, the bottom 
should be an inverted arch. The thickness of the masonry 
of the bottom will depend on the width of the chamber and 
the nature of the soil. Were the soil a solid rock, no bottom- 
ing would be requisite ; if it is of soft material, a very solid 
bottoming, from three to six feet in thickness, may be neces- 
sary. Great care must be taken to prevent the water from 
the upper level filtering through and getting under the bot- 
tom of the lock. 

The lift-wall may have only the same thickness as the side 
walls, but unless the soil is very firm, it would be more pru- 
dent to form a general mass of masonry under the entire 
head-bay, to a level with the base of the chamber founda- 
tions, of which mass the lift- wall should form a part. 

The head-bay is enclosed between two parallel walls, which 
form a part of the side walls of the lock. They are termi- 
nated by two wing walls, m, m, at right angles with the side 
walls. A recess, termed the gate-chamber, is made in the 
wall of the head-bay ; the depth of this recess should be suf- 
ficient to allow the gate, w T hen open, to fall two or three 
inches within the facing of the wall, so that it may be out of 
the way when a boat is passing ; the length of the recess 
should be greater than the width of the gate. That part of 
the recess where the gate turns on its pivot is termed the 
hollow quoin; it receives what is termed the heel or quoin- 
post of the gate, which is made to fit the hollow quoin. The 



460 



CIVIL ENGINEERING. 



distance between the hollow quoins and the face of the lift- 
wall will depend on the pressure against the mitre-sill, and 
the strength of the stone; eighteen inches will generally be 
found sufficient. 

The side walls need not to extend more than twelve inches 
beyond the other end of the gate-chamber. The wing walls 
may be extended back to the total width of the canal, but it 
will be more economical to narrow the canal near the lock, 
and to extend the wing walls only about two feet into the 
banks or sides. The dimensions of the side and wing walls 
of the head-bay are regulated in the same way as the chamber 
w T alls. The top of the side walls of the lock may be from 
one to two feet above the general level of the water in the 
upper level. 

The bottom of the head-bay is flat, and on the same level 
with the bottom of the canal ; the exterior course of stones at 
the entrance to the lock should be so jointed as not to work 
loose. 

The side walls of the tail-bay are also a part of the general 
side walls, and their thickness is regulated as in the preceding 
cases. Their length will depend chiefly on the pressure which 
the lower gates throw against them when the lock is full, and 
partly on the space required by the lockmen in opening and 
shutting the gates. These walls are also terminated by wing 
walls, n, n, similarly arranged to those of the head-bay. The 
points of junction between the wing and side walls should, in 
both cases, either be curved or the stones at the angles be 
rounded off. One or two perpendicular grooves are sometimes 
made in the side walls of the tail-bay, to receive stop-planks, 
when a temporary dam is needed, to shut off the water of the 
lower level from the chamber, in case of repairs, etc. 

The gate-chambers for the lower gates are made in the 
chamber walls ; the bottom of the chamber, where the gates 
swing back, should be flat, or be otherwise arranged so as 
not to impede the play of the gates. 

The bottom of the tail-bay is arranged, in all respects, like 
that of the head-bay. 

639. Those parts of the lock where there is great wear and 
tear, as at the angles generally, should be of cut-stone ; or 
where an accurate finish is indispensable, as at the hollow 
quoins. The other parts may be of brick, rubble, concrete, 
etc., but every part should be laid in cement or the best 
hydraulic mortar. 

The mitre-sills are generally faced with timber, to enable 
them to withstand better the blows which they receive from 
the gates, and to make a tighter joint. 



LOOK GATES. 461 

640. The locks are filled and emptied through sluices in 
the head and tail-gates, opened and closed by slide-valves, or 
by culverts made of masonry or iron pipe placed as shown 
in the figures at c, c, o, etc. The latter is the method gener- 
ally recommended. From the difficulty of repairing them 
when they get out of order, many prefer the use of valves 
in the gates. 

The bottom of the canal below the lock should be protected 
by what is termed an apron, which is a covering of plank 
laid on a grillage, or of dry stone. The length will depend 
upon the strength of the current ; generally a distance of 
from fifteen to thirty feet will be sufficient. 

641. Lock gates. — The gates may be made of wood or of 
iron. Ea^h gate is ordinarily composed of two leaves, each 
leaf consisting of a framework, covered with planking or iron 
plates. The frame, when of timber, consists usually of two 
uprights, connected by, horizontal pieces let into the uprights 
with the usual diagonal bracing. 

In gates of this kind, each leaf turns about an upright, 
which is called the quoin or heel-post. This post is cylin- 
drical on the side next to the hollow quoins, which it exactly 
fits when the gate is shut. It is made slightly eccentric, so 
that when the gate is opened it may turn easily without rub- 
bing against the quoin. At its lower end it rests on a pivot, 
and its upper end turns in a circular collar which is strongly 
anchored in the masonry of the side walls. One of the 
anchor-irons is usually placed in a line with the leaf when 
shut, the other in a line with it when open ; these being the 
best positions to resist most effectually the strain produced 
by the gate. The opposite upright, termed the mitre-post, 
has one edge bevelled off, to fit against the mitre-post of the 
other leaf of the gate, forming a tight joint when the gate is 
shut. 

A long, heavy beam, termed a balance beam from its 
partially balaucing the weight of the leaf, is framed upon the 
quoin-post, and is mortised into the mitre-post. The balance 
beam should be about four feet above the top of the lock ; its 
principal use being to bring the centre of gravity of the leaf 
near the heel-post and to act as a lever to open and shut the 
leaf. 

Sometimes this bar is dispensed with, and the leaves are 
supported on rollers placed under the lower side to assist the 
pivot in supporting their weight. These rollers run on iron 
rails placed on the floor of the gate-chamber. In these cases 
the gates are ordinarily opened and shut by means of wind- 
lasses and chains. This is the method generally used for 



462 CIVIL ENGINEERING. 

very large gates. Gates formed of a single leaf moving on a 
horizontal axis are frequently used. 

642. Inclined planes. — Instead of locks, inclined planes 
are sometimes used, by means of which the boats are passed 
from one level to another. In these cases, water-tight cais- 
sons or cradles, on wheels are used. 

At the places where the levels are to be connected, the 
canal is deepened to admit of the caisson or the cradle to run 
in under the boat to be transferred. Two parallel lines of 
rails start from the bottom of the lower level, ascend an in- 
clined plane up to a summit a little above the upper level, 
and then descend by a short inclined plane into the upper 
level. Two caissons or cradles, one on each set of rails, are 
connected by a wire rope, so that one ascends while the other 
descends. Power being applied, the boats are transferred to 
the appropriate levels. 

The caissons are preferred because they balance each other 
at all times on the inclined plane, whether the boats are light 
or heavy, as they displace exactly their own weight of water 
in the caisson. In some cases, the lifts have been made ver- 
tical instead of inclined planes. 

643. Guard lock. — A large basin is usually formed at 
the outlet, .for the convenience of commerce; and the en- 
trance from this basin to the canal, or from the river to the 
basin, is effected by means of a lock with double gates, so 
arranged that a boat can be passed either way, according as 
the level in the one is higher or lower than that in the other. 
A lock so arranged is termed a tide or guard lock, from its 
uses. The position of the tail of this lock is not indifferent 
in all cases where it forms the outlet to the river ; for were 
the tail placed up stream, it would generally be more difficult 
to pass in or out than if it were down stream. 

644. Lift of locks. — The vertical distance through which 
a boat is raised or lowered by means of the lock is called the 
" lift." This vertical distance between two levels may be 
overcome by the use of a single lock or by a " flight of locks." 
The lift of a single lock ranges from two to twelve feet, but 
generally in ordinary canals is taken at about eight feet. 
Where a greater distance than twelve feet has to bo over- 
come, two or more, or a flight of locks, are necessary. 

In fixing the lengths of the levels and the positions of the 
locks, the engineer, if considering the expenditure of water, 
will prefer single locks, with levels between them, to a flight 
of locks. 

In uiost cases, a flight is cheaper than the same number of 
single locks, as there are certain parts of the masonry which 



WATER SUPPLY. 463 

can be omitted. There is also.an economy in the omission of 
the small gates, which are not needed in flights. It is, how- 
ever, more difficult to secure the foundations of combined 
than of single locks from the effects of the water, which 
forces its way from the upper to the lower level under the 
locks. Where an active trade is carried on, a double flight is 
sometimes arranged, one for the ascending, the other for the 
descending boats. In this case the water which fills one flight 
may, after the passage of the boat, be partly used for the 
other, by an arrangement of valves made in the side wall 
separating the locks. 

The engineer is not always left free to select between the 
two ; for the form of the natural surface may require him to 
adopt a flight at certain points. In a flight the lifts are 
made the same throughout, but in single locks the lifts vary 
according to circumstances. Locks with great lifts consume 
more water, require more care in their construction, and re- 
quire greater care against accidents than the smaller ones, 
but cost less for the same difference of level. 

645. Levels. — The position and the dimensions of the 
levels must be mainly determined by the form of the natural 
surface. By a suitable modification of its cross-section, a 
level can be made as short as may be deemed desirable ; there 
being but one point to be attended to in this, which is, that a 
boat passing between the two locks, at the ends of the level, 
will have time to enter either lock before it can ground, on 
the supposition that the water drawn off to fill the lower lock, 
while the boat is traversing the level, will just reduce the 
depth to the draught of the boat. 

646. Water supply. — Two questions are to be considered : 
the quantity of water required, and the sources of supply. 

The quantity of water required may be divided into two 
portions : 1st. The quantity required for the summit level, 
and those levels which draw from it their supply. 2d. The 
quantity which is wanted for the levels below those, and 
which is furnished from other sources. 

The supply of the first portion, which must be collected at 
the summit level, may be divided into several elements: 1st. 
The quantity required to fill the summit level, and the levels 
which draw their supply from it. 2d. The quantity required 
to supply losses, arising from accidents ; as breaches in the 
banks and the emptying of the levels for repairs. 3d. The 
supplies for losses from surface evaporation, from leakage 
through the soil, and through the lock gates. 4. The quan- 
tity required for the service of the navigation, arising from 
the passage of the boats from one level to another. 



464 CIVIL ENGINEERING. 

The quantity required to fill the summit level and its de- 
pendent levels will depend on their size, an element which 
can be readily calculated; and upon the quantity which 
would soak into the soil, which is an element of a very inde- 
terminate character, depending on the nature of the soil in 
the different levels. 

The supplies for accidental losses are of a still less deter- 
minate character. 

The supply for losses from surface evaporation may be de- 
termined by observations on the rain- fall of the district, and 
the yearly amount of evaporation. Losses caused by leakage 
through the soil will depend on the greater or less capacity 
which the soil has for holding water. This element varies 
not only with the nature of the soil, but also with the shorter 
or longer time that the canal may have been in use; it having 
been found to decrease with time, and to be, comparatively, 
but trifling in old canals. In ordinary soils it may be esti- 
mated at about two inches in depth every twenty-four hours, for 
some time after the canal is first opened. The leakage through 
the gates will depend on the workmanship of these parts. 

In estimating the quantity of water expended for the ser- 
vice of the navigation, in passing the boats from one level to 
another, two distinct cases require examination : 1st. Where 
there is but one lock; and 2d. Where there are several con- 
tiguous locks, or, as it is termed, a flight of locks between 
two levels. 

To pass a boat from one level to the other — from the lower 
to the upper end, for example — the lower gates are opened, 
and the boat having entered the lock they are shut, and water 
is drawn from the upper level to fill the lock and raise the 
boat ; when this operation is finished, the upper gates are 
opened and the boat is passed out. To descend from the 
upper level, the lock is first filled ; the upper gates are then 
opened and the boat passed in ; these gates are next shut, and 
the water is drawn from the lock until the boat is lowered to 
the lower level, when the lower gates are opened and the boat 
is passed out. 

Ilence, to pass a boat, up or down, a quantity of water 
must be drawn from the upper level to fill the lock to a height 
which is equal to the difference of level between the surface 
of the water in the two; this volume of water required to 
pass a boat up or down is termed the prism of lift. The 
calculation, therefore, for the quantity of water requisite For 
the service of the navigation, will be simply thai of the 
number of prisms of lift which each boat wiil draw from the 
summit level in passing up and down. 



WATEB SUPPLY. 405 

An examination of the quantity of water used in passing 
from one level to another, will show that the quantity required 
for a flight of locks is greater than that required for isolated 
locks. 

The source of supply of water is the rain-fall. The rain- 
water which escapes evaporation on the surface and absorp- 
tion by vegetable growth, either runs directly from the surface 
of the ground into streams, or sinks into the ground, Hows 
through crevices of porous strata and escapes by springs, or 
collects in the strata, from which it is drawn by means of weUs. 

647. In whatever way the water may be collected, the 
measurement of the rain-fall of the district from which it 
comes is of the first importance. To make this measurement, 
the area of the district called the drainage area or catchment 
basin, and the depth of the rain-fall for a given time must be 
determined. 

Drainage area. — This area is generally a district of country 
enclosed by a ridge or water-shed line which is continuous 
except at the place where the waters of the basin find an 
outlet. It may be divided by branch ridges or spurs into a 
number of smaller basins, each drained by a stream which 
runs into the main stream. 

Depth of rain-fall. — The depth is determined by estab- 
lishing rain-gauges in the district and having careful obser- 
vations made for as long a period as possible. 

The important points to be determined are : 1. The least 
annual rain-fall; 2. The- mean annual rain-fall ; 3. The great- 
est annual rain-fall ; 4. The distribution of the rain-fall 
throughout the year ; 5. The greatest continuous rain-fall in 
a short period. 

For canal purposes, the least annual rain-fall and the 
longest drought are the most important points to be known. 

Knowing the depth of the rain-fall and the area of the 
catchment basin, an estimate of the amount of water which 
may be available for the canal may be made. Theoretically 
considered, all the water that drains from the ground adjacent 
to the summit level, and above it, might be collected for its 
supply ; but it is found in practice that channels for the con- 
veyance of water must have certain slopes, and that these 
slopes, moreover, will regulate the supply furnished in a cer- 
tain time, all other things being equal. The actual discharge 
of the streams should be measured so as to find the actual 
proportion of available to total rain-fall, and the streams 
should be measured at the same time the rain-gauge observa- 
tions are made. 

The measurement of tlfe quantity of water discharged bv a 
30 



4:66 CIVIL ENGINEERING. 

stream is called " gauging," and to be of value should be made 
with accuracy and extend through some considerable time. 

64:8. Feeders and reservoirs. — The usual method of col- 
lecting the water, and conveying it to the summit level, is 
by feeders and reservoirs. The feeder is a canal of a small 
cross-section, which is traced on the surface of the ground 
with a suitable slope, to convey the water either into the 
reservoir, or direct to the summit level. The dimensions of 
the cross-section, and the longitudinal slope of the feeder, 
should bear certain relations to each other, in order that it 
shall deliver a certain supply in a given time. The smaller 
the slope given to the feeder, the lower will be the points at 
which it will intersect the sources of supply, and therefore 
the greater will be the quantity of w T ater which it will re- 
ceive. The minimum slope, however, has a practical limit, 
which is laid down at four inches in 1,000 yards, or nine 
thousand base to one altitude ; and the maximum slope should 
not be so great as to give the current a velocity which would 
injure the bed of the feeder. Feeders are furnished, like 
ordinary canals, with contrivances to let oft a part, or the 
whole, of the water in them, in cases of heavy rains, or for 
making repairs. 

A reservoir is a place for storing water to be held in re- 
serve for the necessary supply of the summit level. A reser- 
voir is usually formed by choosing a suitable site in a deep 
and narrow valley, which lies above the summit level, and 
erecting a dam of earth, or of masonry, across the outlet of 
the valley, or at some more suitable point, to confine the water 
to be collected. The object to be obtained is to collect the 
greatest volume of water, and at the same time present the 
smallest evaporating surface, at the smallest cost for the con- 
struction of the dam. 

649. Dams. — The dams of reservoirs have been variously 
constructed : in some cases they have been made entirely of 
earth; in others, entirely of masonry ; and in others, of earth 
packed in between parallel stone walls. It is now thought 
best to use either earth or masonry alone, according to the 
circumstances of the case ; the comparative expense of the 
two methods being carefully considered. 

Earthen dams should be made with extreme care, of the 
best binding earth, w r ell freed from everything that might 
cause nitrations. 

The foundation is prepared by stripping off the soil and 
excavating and removing all porous materials, such as sand, 
gravel, and fissured rock, until a compact and water-tight bei 
is reached. * 



DAMS. 



467 



A culvert for the outlet-pipes is next built. This should 
rest on a foundation of concrete and should have the masonry 
laid in cement or the best of hydraulic mortar. It should be 
well coaled with a clay puddling. Frequently the inner end 
of the culvert terminates in a vertical tower, which contains 
outlet-pipes for drawing water from different levels, and the 
necessary mechanism by means of which the pipes can be 
closed or opened. Sometimes a cast-iron pipe alone is laid 
without any culvert. 

The earth is then carefully spread in layers not over a foot 
thick and rammed. A " puddle-wall " with a thickness at the 
base of about one-third its height and diminishing to about 
half this thickness at the top, should form the central part of 
the dam. Care should be taken that it forms a water-tight 
joint with the foundation and also with the puddle coating 
of the culvert. 

The dam may be from fifteen to twenty feet thick at top. 
The slope of the dam towards the pond should be from three 
to six base to one perpendicular; the reverse slope need only 
be somewhat less than the natural slope of the earth. 

The outer slope is usually protected from the weather by 
being covered with sods of grass. The inner slope is usually 
faced with dry stone, to protect the dam from the action of 
the surface ripple. 




Fig. 237. — A, body of the dam. 

<2, top of the waste -weir. 

b, pool, formed by a stop-plank dam at c, to break the fall of the 

water. 
d, covering of loose stone to break the fall of the water from the 

pool above. 



Masonry dams are water-tight walls, of suitable forms 
and dimensions to prevent filtration, and to resist the pressure 
of water in the reservoir. The cross-section is usually that of 
a trapezoid, the face towards the water being vertical, and the 
exterior face inclined with a suitable batter to give the wall 
sufficient stability. The wall should be at least four feet thick 



468 CIVIL ENGINEERING. 

at the water line, to prevent filtration, and this thickness may 
be increased as circumstances may require. 

650. Waste-weirs. — Suitable dispositions should be made 
to relieve the dam from all surplus water during wet seasons. 
For this purpose arrangements should be made for cutting off 
the sources of supply from the reservoir ; and a cut, termed a 
waste-weir (Fig. 237), of suitable width and depth, should 
be made at some point along the top of the dam, and be faced 
with stone, or wood, to give an outlet to the water over the 
dam. In high dams the total fall of the water should be 
divided into several partial falls, by dividing the exterior 
surface over which the water runs into offsets. To break the 
shock of the water upon the horizontal surface of the offset, 
it should be covered with a sheet of water retained by a dam 
placed across its outlet. 

In extensive reservoirs, in which a large surface is exposed 
to the action of the winds, waves might be forced over the 
top of the dam, and subject it to danger; in such cases the 
precaution should be taken of placing a parapet wall towards 
the outer edge of the top of the dam, and facing the top 
throughout with fiat stones laid in mortar. 

651. Water-courses intersecting the line of the canal. 
— The disposition of the natural water-courses which intersect 
the line of the canal will depend on their size, the character 
of their current, and the relative positions of the canal and 
stream. 

Small streams which lie lower than the canal may be con- 
veyed under it through an ordinary culvert. If the level of 
the canal and stream is nearly the same, it may be conveyed 
under the canal by an inverted syphon of masonry or iron, 
usually termed a broken-back culvert, or if the water of the 
stream is limpid, and its current gentle, it may be received 
into the canal. Its communication with the canal should be 
so arranged that the water may be shut off or let in at plea- 
sure, in any quantity desired. 

In cases where the line of the canal is crossed by a torrent, 
which brings down a large quantity of sand, pebbles, etc., it 
may be necessary to make a permanent structure over the 
canal, forming a channel for the torrent ; but if the discharge 
of the torrent is only periodical, a movable channel may be 
arranged, for the same purpose, by constructing a boat with 
a deck and sides to form the water-way of the torrent. The 
boat is kept in a recess in the canal near the point where it 
is used, and is floated to its position, and sunk when wanted. 

When the line of the canal is intersected by a wide water- 
course, the communication between the two shores must be 



IRRIGATING CANALS. 469 

effected either by a canal aqueduct bridge, or by the boats 
descending from the canal into the stream. 

652. Dimensions of canals and their locks in the United 
States. — The original dimensions of the New York Eric Canal 
and its locks have been generally adopted for similar works 
subsequently constructed in most of the other States. The 
dimensions of this canal and its locks were as follows : 

Width of canal at top 40 feet. 

Width at bottom 28 " 

Depth of water 4 " 

Width of tow-path 9 to 12 " 

Length of locks between mitre-sills 90 " ■ 

Width of locks 15 " 

For the enlargement of the Erie Canal, the following are 
the dimensions : 

Width of canal at top 70 feet. 

Width at bottom 42 " 

Depth of water 7 " 

Width of tow-path 14 " 

Length of locks between mitre-sills 110 " 

Width of lock at top 18.8 " 

Width of lock at bottom 14.6 " 

Lift of locks 8 " 

Between the double locks a culvert is placed, which allows 
the water to flow from the level above the lock to the one 
below, when there is a surplus of water in the former. 



IRRIGATING CANALS. 

653. Canals belonging to this class are used to bring from 
its source' a supply of water, which, when reaching certa^i 
localities, is made to flow over the land for agricultural pui> 
poses. This kind of canal is practically unknown in the 
United States, as the farmer depends almost entirely on the 
rain-fall alone for the requisite amount of moisture for his 
crops. 

Irrigation canals of large size have been used in India for 
hundreds of years ; they are also found in Italy. Rude imi- 
tations, of small size, are to be seen in Mexico, the territory 
of New Mexico, lower part of California, and other parts of 
the United States. 

In certain parts of our country they could be used to great 



4:70 CIVIL ENGINEERING. 

advantage, and since in the future they may be used, it is 
thought advisable to allude briefly to them in this treatise. 

The special difference between a navigable canal and an 
irrigation one is that the former requires that there should be 
little or no current in the canal, so that navigation may be 
easy in •both directions, while the latter requires that the 
canal should be a running stream, fed by continuous supplies 
of water at its source, to make up the losses caused by the 
amounts of water drawn off from the canal for the purposes 
of irrigation. 

Hence, for two canals of the same size, the navigable 
canal will require a less volume of water than the irriga- 
tion canal, and is more economically constructed on a low 
level. 

The irrigation canal should be carried at as high a level as 
possible, so as to have sufficient fall for the water which is to 
be used to irrigate the land on both sides of it and at con- 
siderable distances from it. This irrigation is effected by 
means of branch canals leading from the main one, whence 
the water is carried by small channels on the fields. 

654. The problem of an irrigation canal is to so connect it 
with the stream furnishing the supply of water, and to so 
arrange the slope of the bed of the canal, that the canal 
shall not become choked with silt. 

A canal opening direct into the stream which supplies it 
with water, if proper arrangements are not made, will be lia- 
ble to have the volume of water greatly increased in time of 
freshets, and at other times have the supply entirely cut off. 
In the first case, large quantities of silt would be washed into 
the canal, choking it up as the water receded to its proper 
level. In the second case, the supply would probably fail at 
the critical period of the growing crops when water was 
greatly needed. 

A good selection of the point where the canal joins the 
stream, and the use of sluices to govern the supply of 
water, will greatly prevent the occurrence of either of these 
conditions. 

To prevent the silting up of the canal, the slope of the bed 
is so fixed that the water shall have a uniform velocity 
throughout. It is therefore seen that, as the water is drawn 
off at different points for the irrigation of the land, on the 
right and left of the canal, the volume of water is reduced. 
The portions of the canal below these points must then be so 
iixed as to preserve the same rate of motion in the water. 
This is done by decreasing the width and -depth of the canal, 
and increasing the slope of the bed. Thus starting* with a 



DRAINAGE CANALS. 471 

water-way 100 feet wide, 6 feet deep, and a slope of 6 inches 
to the mile, the width of water-way being contracted to 80, 
60, 40, and 20 feet by the water being drawn off with the 
corresponding depths, 5£, 5, 4-J, and 4 feet ; the slopes the 
bed should have to keep the velocity uniform would be 6.4, 
7, 7.9, and 10.3 inches per mile. 

655. An irrigation canal may be used for the purposes of 
navigation. In which case the principles already laid down 
for that class of canals equally apply, with the condition, how- 
ever, that the velocity of the current in the canal should not 
be so slight as to injure its uses as an irrigation canal, nor so 
swift as to offer too great a resistance to the boats using it 
as a navigable canal. 



DRAINAGE CANALS. 

656. Canals of this class are the reverse of the last class. 
They are used to carry off the superfluous water which falls 
on or flows over the land. 

The water-levels of canals for drainage, to be effective, 
should at all times be at least three feet below the level of 
the ground. 

Each channel for the water should have sufficient area and 
declivity, when subjected to the most unfavorable conditions, 
to discharge all the water that it receives as fast as this water 
flows in, without its water-level rising so high as to obstruct 
the flow from its branches or flood the country. 

Hence it is seen that to plan such a system the greatest 
annual rain-fall of the district, and the greatest fall in a short 
period or flood must be known. 

Where the land to be drained is below the level of high 
water, the area to-be drained must be protected by embank- 
ments. The canals are then laid off, on the plan just given, 
and the water from the main canals removed by pumping. 

Drainage canals may be divided into two classes : open 
and covered. Where pure water is to be removed, the former 
are used ; when filthy water, or foul materials, are to be re- 
moved, the latter are used, and are known as sewers. Sewer- 
age is the special name used to designate the drainage of a 
city or town, in which the foul waters and refuse are collected 
and discharged by sewers. 

As far as the principles of construction are concerned they 
do not differ from the works already described. Especial at- 
tention must be paid to prevent the escape of the foul gas 
and disagreeable odors from the drains. 



472 CIVIL ENGINEERING. 



CANALS FOR SUPPLYING CITIES AND TOWNS WITH WATER. 

657. As sewers are only particular cases of drainage canals, 
so are canals for supplying cities with water only particular 
cases of irrigation canals, and are governed by the same 
general principles in their construction. 

The canals of this class are usually covered, and receive the 
general name of aqueducts. 

658. The health and comfort of the residents of cities and 
towns are so dependent upon a proper supply of water and a 
good system of sewerage that the greatest care must be taken 
by the engineer that no mistakes are made by him in planning 
and constructing either of these systems. The principles 
which regulate in deciding upon the quantity of water re- 
quired, the means and purity of the supply, the location of the 
reservoirs, the method of distribution, etc., form a subject 
which can be considered in a special treatise only. The same 
remark applies also to sewerage. 



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